text:
# Expected behavior of an algorithm to minimize rankings

Suppose $$n$$ students have preferences over $$n$$ different notebooks. Their preferences can be represented with a square matrix of size $$n$$ where each column is a different permutation of the vector $$[1:n]$$, where the first entry in the column represents the most desirable notebook for student 1, and so on. We are interested in the assignment of the notebooks to students that minimizes the sum of rankings.

For example, such allocation in the problem below

  1    2    2
2    1    3
3    3    1

would be the allocation (1,2,3) with a ranking sum of 1+1+2=4.

My two questions are the following. If the matrix with preferences is chosen uniformly at random, what is the expected sum of rankings in the assignment that minimizes the sum of rankings?

Second, I can answer this question by running a simulation, but is there a known algorithm that efficiently finds the allocation that minimizes the sum of rankings?

Idea: In the best-case scenario, this sum is $$n$$. In the worst-case scenario, where each column is identical, the sum is $$n(n+1)/2$$. The expectation over all possible cases must be somewhere in between.

• Doesn't the allocation 1,2,3 have value 1+1+1=3? Apr 9, 2021 at 18:02
• @YuvalFilmus Each column, not row is the preference of one student. Apr 9, 2021 at 18:54
• But $1,2,3$ is the diagonal. Apr 9, 2021 at 18:55
• – D.W.
Apr 27, 2021 at 23:24

Finding the minimum matching is known as the assignment problem, and it has efficient solutions.

Your exact problem has been considered by Parviainen, Random assignment with integer costs — it's his "Case I". Parviainen showed that the expected value is between $$\frac{\pi^2}{6} n$$ and $$2n$$, and his simulation results suggest an intermediate value $$cn$$, where $$c \approx 1.830$$. See also the survey by Krochmal and Pardalos, Random assignment problems.

• Wikipedia summarizes the known algorithms. There are libraries implementing some of them. Apr 12, 2021 at 9:31
• Thanks. Just to make sure I get it: even as the number of students grows, the expected ranking of the notebook they each get is CONSTANT and around 1.83? This is remarkable that does not depend on n!
– fox
Apr 12, 2021 at 9:56
• It is quite amazing. One way to see it is that if you keep only a short prefix of each ranking, then you can still find a matching of almost maximal size. Apr 12, 2021 at 10:34
• Sorry for bothering, but are you familiar with any results regarding the expected maximum ranking? This is, what is the ranking realized for the worst student? We know on average is 1.8, but for the worst it seems 6.44 for 100 students and 7.04 for 200 students. Any idea on a theoretical result for this?
– fox
Apr 27, 2021 at 10:59
• If you’re interested in a different question, how about asking it as a new post? Apr 27, 2021 at 11:01

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## 5G NR QC-LDPC Encoding Algorithm

3GPP 5G has been focused on structured LDPC codes known as quasi-cyclic low-density parity-check (QC-LDPC) codes, which exhibit advantages over other types of LDPC codes with respect to the hardware implementations of encoding and decoding using...

## Interpolation Basics

This article covers interpolation basics, and provides a numerical example of interpolation of a time signal. Figure 1 illustrates what we mean by interpolation. The top plot shows a continuous time signal, and the middle plot shows a sampled version with sample time Ts. The goal of interpolation is to increase the sample rate such that the new (interpolated) sample values are close to the values of the continuous signal at the sample times [1]. For example, if we increase the sample rate by the integer factor of four, the interpolated signal is as shown in the bottom plot. The time between samples has been decreased from Ts to Ts/4.

## Round-robin or RTOS for my embedded system

First of all, I would like to introduce myself. I am Manuel Herrera. I am starting to write blogs about the situations that I have faced over the years of my career and discussed with colleagues.To begin, I would like to open a conversation...

## Somewhat Off Topic: Deciphering Transistor Terminology

I recently learned something mildly interesting about transistors, so I thought I'd share my new knowledge with you folks. Figure 1 shows a p-n-p transistor comprising a small block of n-type semiconductor sandwiched between two blocks of p-type...

Digital Signal Processing (DSP) technology is the cornerstone of most cutting edge technology today. For example, digital signal processing drives much of machine learning in artificial intelligence (AI). It also steers eyesight and movement...

## Generating Partially Correlated Random Variables

IntroductionIt is often useful to be able to generate two or more signals with specific cross-correlations. Or, more generally, we would like to specify an $\left(N \times N\right)$ covariance matrix, $\mathbf{R}_{xx}$, and generate $N$ signals...

## A Brief Introduction To Romberg Integration

This article briefly describes a remarkable integration algorithm, called "Romberg integration." The algorithm is used in the field of numerical analysis but it's not so well-known in the world of DSP.

## Evaluate Window Functions for the Discrete Fourier Transform

The Discrete Fourier Transform (DFT) operates on a finite length time sequence to compute its spectrum.  For a continuous signal like a sinewave, you need to capture a segment of the signal in order to perform the DFT.  Usually, you...

## Feedback Controllers - Making Hardware with Firmware. Part 10. DSP/FPGAs Behaving Irrationally

This article will look at a design approach for feedback controllers featuring  low-latency "irrational" characteristics to enable the creation of physical components such as transmission lines. Some thought will also be given as to...


text:
pyiron.dft.waves.dos module¶

class pyiron.dft.waves.dos.Dos(n_bins=100, es_obj=None, eigenvalues=None, bin_density=None)[source]

Bases: object

The DOS class stores all information to store and retrieve the total and resolved density of states from an electronic structure calculation.

Parameters
• n_bins (int) – Number of histogram bins required to calculate the DOS

• es_obj – The pyiron.objects.waves.core.ElectronicStructure instance for which the DOS has to be computed

• eigenvalues (list/numpy.ndarray) – If es-obj is None, the eigenvalues could be specified as a list

get_orbital_resolved_dos(orbital_indices, spin_indices=0)[source]

Gives the dos contribution of a given indices of orbitals as arranged in the pyiron.objects.waves.ElectronicStructure instance.

Parameters
• orbital_indices (list/numpy.ndarray) – The index/indices of the orbitals for which the dos contribution is required

• spin_indices (list/numpy.ndarray) – The index/indices of the spins for which the dos contribution is required

Returns

The required dos

Return type

numpy.ndaray

get_spatial_orbital_resolved_dos(atom_indices, orbital_indices, spin_indices=0)[source]

Gives the dos contribution of a given indices of atoms as well as orbitals as arranged in the pyiron.objects.waves.ElectronicStructure instance.

Parameters
• atom_indices (list/numpy.ndarray) – The index/indices of the atoms for which the dos contribution is required

• orbital_indices (list/numpy.ndarray) – The index/indices of the orbitals for which the dos contribution is required

• spin_indices (list/numpy.ndarray) – The index/indices of the spins for which the dos contribution is required

Returns

The required dos

Return type

numpy.ndaray

get_spatially_resolved_dos(atom_indices, spin_indices=0)[source]

Gives the dos contribution of a given indices of atoms as arranged in the pyiron.objects.waves.ElectronicStructure instance.

Parameters
• atom_indices (list/numpy.ndarray) – The index/indices of the atoms for which the dos contribution is required

• spin_indices (list/numpy.ndarray) – The index/indices of the spins for which the dos contribution is required

Returns

The required dos

Return type

numpy.ndarray

get_spin_resolved_dos(spin_indices)[source]

Gives the dos contribution of a given indices of spin as arranged in the pyiron.objects.waves.ElectronicStructure instance.

Parameters

spin_indices (list/numpy.ndarray) – The index/indices of the spins for which the dos contribution is required

Returns

The required dos

Return type

numpy.ndarray

plot_orbital_resolved_dos(**kwargs)[source]

Plots the orbital resolved DOS

Parameters

**kwargs – Variable for matplotlib.pylab.plot customization (linewidth, linestyle, etc.)

Returns

matplotlib.pylab.plot

plot_total_dos(**kwargs)[source]

Plots the total DOS

Parameters

**kwargs – Variables for matplotlib.pylab.plot customization (linewidth, linestyle, etc.)

Returns

matplotlib.pylab.plot

exception pyiron.dft.waves.dos.NoResolvedDosError[source]

Bases: Exception

Raised when information on the resolved dos in unavailable


text:
Under the auspices of the Computational Complexity Foundation (CCF)

REPORTS > KEYWORD > ARITHMETIC CIRCUITS:
Reports tagged with arithmetic circuits:
TR98-019 | 5th April 1998
Eric Allender, Klaus Reinhardt

#### Isolation, Matching, and Counting

We show that the perfect matching problem is in the
complexity class SPL (in the nonuniform setting).
This provides a better upper bound on the complexity of the
matching problem, as well as providing motivation for studying
the complexity class SPL.

Using similar ... more >>>

TR98-020 | 10th April 1998
Andris Ambainis, David Mix Barrington, Huong LeThanh

#### On Counting $AC^0$ Circuits with Negative Constants

Continuing the study of the relationship between $TC^0$,
$AC^0$ and arithmetic circuits, started by Agrawal et al.
(IEEE Conference on Computational Complexity'97),
we answer a few questions left open in this
paper. Our main result is that the classes Diff$AC^0$ and
Gap$AC^0$ ... more >>>

TR98-023 | 16th April 1998
Eric Allender, Shiyu Zhou

#### Uniform Inclusions in Nondeterministic Logspace

We show that the complexity class LogFew is contained
in NL $\cap$ SPL. Previously, this was known only to
hold in the nonuniform setting.

more >>>

TR99-012 | 19th April 1999
Eric Allender, Andris Ambainis, David Mix Barrington, Samir Datta, Huong LeThanh

#### Bounded Depth Arithmetic Circuits: Counting and Closure

Constant-depth arithmetic circuits have been defined and studied
in [AAD97,ABL98]; these circuits yield the function classes #AC^0
and GapAC^0. These function classes in turn provide new
characterizations of the computational power of threshold circuits,
and provide a link between the circuit classes AC^0 ... more >>>

TR01-041 | 23rd May 2001
Eric Allender, Michal Koucky, Detlef Ronneburger, Sambuddha Roy, V Vinay

#### Time-Space Tradeoffs in the Counting Hierarchy

We extend the lower bound techniques of [Fortnow], to the
unbounded-error probabilistic model. A key step in the argument
is a generalization of Nepomnjascii's theorem from the Boolean
setting to the arithmetic setting. This generalization is made
possible, due to the recent discovery of logspace-uniform TC^0
more >>>

TR02-012 | 3rd February 2002
Ran Raz

#### On the Complexity of Matrix Product

We prove a lower bound of $\Omega(m^2 \log m)$ for the size of
any arithmetic circuit for the product of two matrices,
over the real or complex numbers, as long as the circuit doesn't
use products with field elements of absolute value larger than 1
(where $m \times m$ is ... more >>>

TR02-052 | 3rd September 2002
Vince Grolmusz

#### Computing Elementary Symmetric Polynomials with a Sub-Polynomial Number of Multiplications

Revisions: 1

Elementary symmetric polynomials $S_n^k$ are used as a
benchmark for the bounded-depth arithmetic circuit model of computation.
In this work we prove that $S_n^k$ modulo composite numbers $m=p_1p_2$
can be computed with much fewer multiplications than over any field, if
the coefficients of monomials $x_{i_1}x_{i_2}\cdots x_{i_k}$ ... more >>>

TR03-018 | 28th March 2003
Matthias Galota, Heribert Vollmer

#### Functions Computable in Polynomial Space

We show that the class of integer-valued functions computable by
polynomial-space Turing machines is exactly the class of functions f
for which there is a nondeterministic polynomial-time Turing
machine with a certain order on its paths that on input x outputs a 3x3
matrix with entries from {-1,0,1} on each ... more >>>

TR05-037 | 8th April 2005
Eric Allender, Peter Bürgisser, Johan Kjeldgaard-Pedersen, Peter Bro Miltersen

#### On the Complexity of Numerical Analysis

We study two quite different approaches to understanding the complexity
of fundamental problems in numerical analysis. We show that both hinge
on the question of understanding the complexity of the following problem,
which we call PosSLP:
Given a division-free straight-line program
producing an integer N, decide whether N>0.
more >>>

TR06-060 | 4th May 2006
Ran Raz, Amir Shpilka, Amir Yehudayoff

#### A Lower Bound for the Size of Syntactically Multilinear Arithmetic Circuits

We construct an explicit polynomial $f(x_1,...,x_n)$, with
coefficients in ${0,1}$, such that the size of any syntactically
multilinear arithmetic circuit computing $f$ is at least
$\Omega( n^{4/3} / log^2(n) )$. The lower bound holds over any field.

more >>>

TR07-005 | 17th January 2007
Rahul Santhanam

#### Circuit Lower Bounds for Merlin-Arthur Classes

We show that for each k > 0, MA/1 (MA with 1 bit of advice) does not have circuits of size n^k. This implies the first superlinear circuit lower bounds for the promise versions of the classes MA, AM and ZPP_{||}^{NP}.

We extend our main result in several ways. For ... more >>>

TR07-087 | 11th July 2007
Nutan Limaye, Meena Mahajan, B. V. Raghavendra Rao

#### Arithmetizing classes around NC^1 and L

The parallel complexity class NC^1 has many equivalent models such as
polynomial size formulae and bounded width branching
programs. Caussinus et al. \cite{CMTV} considered arithmetizations of
two of these classes, #NC^1 and #BWBP. We further this study to
include arithmetization of other classes. In particular, we show that
counting paths ... more >>>

TR07-121 | 21st November 2007
Zeev Dvir, Amir Shpilka, Amir Yehudayoff

#### Hardness-Randomness Tradeoffs for Bounded Depth Arithmetic Circuits

In this paper we show that lower bounds for bounded depth arithmetic circuits imply derandomization of polynomial identity testing for bounded depth arithmetic circuits. More formally, if there exists an explicit polynomial f(x_1,...,x_m) that cannot be computed by a depth d arithmetic circuit of small size then there exists ... more >>>

TR08-001 | 5th January 2008
Ran Raz

#### Elusive Functions and Lower Bounds for Arithmetic Circuits

A basic fact in linear algebra is that the image of the curve
$f(x)=(x^1,x^2,x^3,...,x^m)$, say over $C$, is not contained in any
$m-1$ dimensional affine subspace of $C^m$. In other words, the image
of $f$ is not contained in the image of any polynomial-mapping
$G:C^{m-1} ---> C^m$ ... more >>>

TR08-006 | 18th January 2008
Ran Raz, Amir Yehudayoff

#### Lower Bounds and Separations for Constant Depth Multilinear Circuits

We prove an exponential lower bound for the size of constant depth multilinear arithmetic circuits computing either the determinant or the permanent (a circuit is called multilinear, if the polynomial computed by each of its gates is multilinear). We also prove a super-polynomial separation between the size of product-depth $d$ ... more >>>

TR08-025 | 3rd January 2008
Vikraman Arvind, Partha Mukhopadhyay, Srikanth Srinivasan

#### New results on Noncommutative and Commutative Polynomial Identity Testing

Revisions: 2

Using ideas from automata theory we design a new efficient
(deterministic) identity test for the \emph{noncommutative}
polynomial identity testing problem (first introduced and studied by
Raz-Shpilka in 2005 and Bogdanov-Wee in 2005). More precisely,
given as input a noncommutative
circuit $C(x_1,\cdots,x_n)$ computing a ... more >>>

TR08-048 | 8th April 2008
Meena Mahajan, B. V. Raghavendra Rao

#### Arithmetic circuits, syntactic multilinearity, and the limitations of skew formulae

Functions in arithmetic NC1 are known to have equivalent constant
width polynomial degree circuits, but the converse containment is
unknown. In a partial answer to this question, we show that syntactic
multilinear circuits of constant width and polynomial degree can be
depth-reduced, though the resulting circuits need not be ... more >>>

TR08-062 | 11th June 2008
Manindra Agrawal, V Vinay

#### Arithmetic Circuits: A Chasm at Depth Four

We show that proving exponential lower bounds on depth four arithmetic
circuits imply exponential lower bounds for unrestricted depth arithmetic
circuits. In other words, for exponential sized circuits additional depth
beyond four does not help.

We then show that a complete black-box derandomization of Identity Testing problem for depth four ... more >>>

TR09-032 | 16th April 2009
Neeraj Kayal, Shubhangi Saraf

#### Blackbox Polynomial Identity Testing for Depth 3 Circuits

We study depth three arithmetic circuits with bounded top fanin. We give the first deterministic polynomial time blackbox identity test for depth three circuits with bounded top fanin over the field of rational numbers, thus resolving a question posed by Klivans and Spielman (STOC 2001).

Our main technical result is ... more >>>

TR09-116 | 15th November 2009
Zohar Karnin, Partha Mukhopadhyay, Amir Shpilka, Ilya Volkovich

#### Deterministic identity testing of depth 4 multilinear circuits with bounded top fan-in

We give the first sub-exponential time deterministic polynomial
identity testing algorithm for depth-$4$ multilinear circuits with
a small top fan-in. More accurately, our algorithm works for
depth-$4$ circuits with a plus gate at the top (also known as
$\Spsp$ circuits) and has a running time of
$\exp(\poly(\log(n),\log(s),k))$ where $n$ is ... more >>>

TR09-134 | 10th December 2009
Zeev Dvir

#### On matrix rigidity and locally self-correctable codes

Revisions: 1

We describe a new approach for the problem of finding {\rm rigid} matrices, as posed by Valiant [Val77], by connecting it to the, seemingly unrelated, problem of proving lower bounds for locally self-correctable codes. This approach, if successful, could lead to a non-natural property (in the sense of Razborov and ... more >>>

TR10-103 | 28th June 2010
Andreas Krebs, Nutan Limaye, Meena Mahajan

#### Counting paths in VPA is complete for \#NC$^1$

We give a \#NC$^1$ upper bound for the problem of counting accepting paths in any fixed visibly pushdown automaton. Our algorithm involves a non-trivial adaptation of the arithmetic formula evaluation algorithm of Buss, Cook, Gupta, Ramachandran (BCGR: SICOMP 21(4), 1992). We also show that the problem is \#NC$^1$ hard. Our ... more >>>

TR10-105 | 29th June 2010
Scott Aaronson, Dieter van Melkebeek

#### A note on circuit lower bounds from derandomization

We present an alternate proof of the result by Kabanets and Impagliazzo that derandomizing polynomial identity testing implies circuit lower bounds. Our proof is simpler, scales better, and yields a somewhat stronger result than the original argument.

more >>>

TR10-118 | 27th July 2010
Maurice Jansen

#### Extracting Roots of Arithmetic Circuits by Adapting Numerical Methods

Revisions: 2

For two polynomials $f \in \mathbb{F}[x_1, x_2, \ldots, x_n, y]$ and $p \in \mathbb{F}[x_1, x_2, \ldots, x_n]$, we say that $p$ is a root of $f$, if $f(x_1, x_2, \ldots, x_n, p) \equiv 0$. We study the relation between the arithmetic circuit sizes of $f$ and $p$ for general circuits ... more >>>

TR10-188 | 8th December 2010
Matthew Anderson, Dieter van Melkebeek, Ilya Volkovich

#### Derandomizing Polynomial Identity Testing for Multilinear Constant-Read Formulae

Revisions: 1

We present a polynomial-time deterministic algorithm for testing whether constant-read multilinear arithmetic formulae are identically zero. In such a formula each variable occurs only a constant number of times and each subformula computes a multilinear polynomial. Our algorithm runs in time $s^{O(1)}\cdot n^{k^{O(k)}}$, where $s$ denotes the size of the ... more >>>

TR10-189 | 8th December 2010
Neeraj Kayal, Chandan Saha

#### On the Sum of Square Roots of Polynomials and related problems

The sum of square roots problem over integers is the task of deciding the sign of a nonzero sum, $S = \Sigma_{i=1}^{n}{\delta_i}$ . \sqrt{$a_i$}, where $\delta_i \in$ { +1, -1} and $a_i$'s are positive integers that are upper bounded by $N$ (say). A fundamental open question in numerical analysis and ... more >>>

TR11-021 | 13th February 2011
Chandan Saha, Ramprasad Saptharishi, Nitin Saxena

#### A Case of Depth-3 Identity Testing, Sparse Factorization and Duality

Finding an efficient solution to the general problem of polynomial identity testing (PIT) is a challenging task. In this work, we study the complexity of two special but natural cases of identity testing - first is a case of depth-$3$ PIT, the other of depth-$4$ PIT.

Our first problem is ... more >>>

TR11-022 | 14th February 2011
Malte Beecken, Johannes Mittmann, Nitin Saxena

#### Algebraic Independence and Blackbox Identity Testing

Algebraic independence is an advanced notion in commutative algebra that generalizes independence of linear polynomials to higher degree. Polynomials $\{f_1,\ldots, f_m\} \subset \mathbb{F}[x_1,\ldots, x_n]$ are called algebraically independent if there is no non-zero polynomial $F$ such that $F(f_1, \ldots, f_m) = 0$. The transcendence degree, $\mbox{trdeg}\{f_1,\ldots, f_m\}$, is the maximal ... more >>>

TR11-046 | 2nd April 2011
Shubhangi Saraf, Ilya Volkovich

#### Black-Box Identity Testing of Depth-4 Multilinear Circuits

We study the problem of identity testing for multilinear $\Spsp(k)$ circuits, i.e. multilinear depth-$4$ circuits with fan-in $k$ at the top $+$ gate. We give the first polynomial-time deterministic
identity testing algorithm for such circuits. Our results also hold in the black-box setting.

The running time of our algorithm is ... more >>>

TR11-138 | 24th October 2011
Guy Moshkovitz

#### Complexity Lower Bounds through Balanced Graph Properties

In this paper we present a combinatorial approach for proving complexity lower bounds. We mainly focus on the following instantiation of it. Consider a pair of properties of $m$-edge regular hypergraphs. Suppose they are indistinguishable'' with respect to hypergraphs with $m-t$ edges, in the sense that every such hypergraph has ... more >>>

TR13-026 | 11th February 2013
Ankit Gupta, Pritish Kamath, Neeraj Kayal, Ramprasad Saptharishi

#### Arithmetic circuits: A chasm at depth three

Revisions: 1

We show that, over $\mathbb{C}$, if an $n$-variate polynomial of degree $d = n^{O(1)}$ is computable by an arithmetic circuit of size $s$ (respectively by an algebraic branching program of size $s$) then it can also be computed by a depth three circuit (i.e. a $\Sigma \Pi \Sigma$-circuit) of size ... more >>>

TR13-043 | 25th March 2013
Oded Goldreich, Avi Wigderson

#### On the Size of Depth-Three Boolean Circuits for Computing Multilinear Functions

Revisions: 1

We propose that multi-linear functions of relatively low degree
over GF(2) may be good candidates for obtaining exponential
lower bounds on the size of constant-depth Boolean circuits
(computing explicit functions).
Specifically, we propose to move gradually from linear functions
to multilinear ones, and conjecture that, for any $t\geq2$,
more >>>

TR13-068 | 3rd May 2013
Mrinal Kumar, Shubhangi Saraf

#### Lower Bounds for Depth 4 Homogenous Circuits with Bounded Top Fanin

We study the class of homogenous $\Sigma\Pi\Sigma\Pi(r)$ circuits, which are depth 4 homogenous circuits with top fanin bounded by $r$. We show that any homogenous $\Sigma\Pi\Sigma\Pi(r)$ circuit computing the permanent of an $n\times n$ matrix must have size at least $\exp\left(n^{\Omega(1/r)}\right)$.

In a recent result, Gupta, Kamath, Kayal and ... more >>>

TR13-153 | 8th November 2013
Mrinal Kumar, Shubhangi Saraf

#### The Limits of Depth Reduction for Arithmetic Formulas: It's all about the top fan-in

In recent years, a very exciting and promising method for proving lower bounds for arithmetic circuits has been proposed. This method combines the method of {\it depth reduction} developed in the works of Agrawal-Vinay [AV08], Koiran [Koi12] and Tavenas [Tav13], and the use of the shifted partial derivative complexity measure ... more >>>

TR14-001 | 4th January 2014
Swastik Kopparty, Shubhangi Saraf, Amir Shpilka

#### Equivalence of Polynomial Identity Testing and Deterministic Multivariate Polynomial Factorization

In this paper we show that the problem of deterministically factoring multivariate polynomials reduces to the problem of deterministic polynomial identity testing. Specifically, we show that given an arithmetic circuit (either explicitly or via black-box access) that computes a polynomial $f(X_1,\ldots,X_n)$, the task of computing arithmetic circuits for the factors ... more >>>

TR14-003 | 10th January 2014
Zeev Dvir, Rafael Mendes de Oliveira, Amir Shpilka

#### Testing Equivalence of Polynomials under Shifts

Two polynomials $f, g \in F[x_1, \ldots, x_n]$ are called shift-equivalent if there exists a vector $(a_1, \ldots, a_n) \in {F}^n$ such that the polynomial identity $f(x_1+a_1, \ldots, x_n+a_n) \equiv g(x_1,\ldots,x_n)$ holds. Our main result is a new randomized algorithm that tests whether two given polynomials are shift equivalent. Our ... more >>>

TR14-089 | 16th July 2014
Neeraj Kayal, Chandan Saha

#### Lower Bounds for Depth Three Arithmetic Circuits with small bottom fanin

Revisions: 1

Shpilka and Wigderson (CCC 1999) had posed the problem of proving exponential lower bounds for (nonhomogeneous) depth three arithmetic circuits with bounded bottom fanin over a field $\mathbb{F}$ of characteristic zero. We resolve this problem by proving a $N^{\Omega(\frac{d}{\tau})}$ lower bound for (nonhomogeneous) depth three arithmetic circuits with bottom fanin ... more >>>

TR14-122 | 30th September 2014
Eric Allender, Anna Gal, Ian Mertz

#### Dual VP Classes

Revisions: 2

We consider arithmetic complexity classes that are in some sense dual to the classes VP(Fp) that were introduced by Valiant. This provides new characterizations of the complexity classes ACC^1 and TC^1, and also provides a compelling example of
a class of high-degree polynomials that can be simulated via arithmetic circuits ... more >>>

TR14-130 | 17th October 2014
Ankit Gupta

#### Algebraic Geometric Techniques for Depth-4 PIT & Sylvester-Gallai Conjectures for Varieties

Revisions: 1

We present an algebraic-geometric approach for devising a deterministic polynomial time blackbox identity testing (PIT) algorithm for depth-4 circuits with bounded top fanin. Using our approach, we devise such an algorithm for the case when such circuits have bounded bottom fanin and satisfy a certain non-degeneracy condition. In particular, we ... more >>>

TR14-157 | 27th November 2014
Rafael Mendes de Oliveira, Amir Shpilka, Ben Lee Volk

#### Subexponential Size Hitting Sets for Bounded Depth Multilinear Formulas

In this paper we give subexponential size hitting sets for bounded depth multilinear arithmetic formulas. Using the known relation between black-box PIT and lower bounds we obtain lower bounds for these models.

For depth-3 multilinear formulas, of size $\exp(n^\delta)$, we give a hitting set of size $\exp(\tilde{O}(n^{2/3 + 2\delta/3}))$. ... more >>>

TR15-015 | 30th January 2015
Neeraj Kayal, Chandan Saha

#### Multi-$k$-ic depth three circuit lower bound

In a multi-$k$-ic depth three circuit every variable appears in at most $k$ of the linear polynomials in every product gate of the circuit. This model is a natural generalization of multilinear depth three circuits that allows the formal degree of the circuit to exceed the number of underlying variables ... more >>>

TR15-042 | 30th March 2015
Ilya Volkovich

#### Computations beyond Exponentiation Gates and Applications

In Arithmetic Circuit Complexity the standard operations are $\{+,\times\}$.
Yet, in some scenarios exponentiation gates are considered as well (see e.g. \cite{BshoutyBshouty98,ASSS12,Kayal12,KSS14}).
In this paper we study the question of efficiently evaluating a polynomial given an oracle access to its power.
That is, beyond an exponentiation gate. As ... more >>>

TR15-061 | 14th April 2015
Benny Applebaum, Jonathan Avron, Christina Brzuska

#### Arithmetic Cryptography

Revisions: 1

We study the possibility of computing cryptographic primitives in a fully-black-box arithmetic model over a finite field F. In this model, the input to a cryptographic primitive (e.g., encryption scheme) is given as a sequence of field elements, the honest parties are implemented by arithmetic circuits which make only a ... more >>>

TR15-071 | 23rd April 2015
Mrinal Kumar, Shubhangi Saraf

#### Sums of products of polynomials in few variables : lower bounds and polynomial identity testing

We study the complexity of representing polynomials as a sum of products of polynomials in few variables. More precisely, we study representations of the form $$P = \sum_{i = 1}^T \prod_{j = 1}^d Q_{ij}$$
such that each $Q_{ij}$ is an arbitrary polynomial that depends on at most $s$ variables.

... more >>>

TR15-109 | 1st July 2015

#### An exponential lower bound for homogeneous depth-5 circuits over finite fields

In this paper, we show exponential lower bounds for the class of homogeneous depth-$5$ circuits over all small finite fields. More formally, we show that there is an explicit family $\{P_d : d \in N\}$ of polynomials in $VNP$, where $P_d$ is of degree $d$ in $n = d^{O(1)}$ variables, ... more >>>

TR15-115 | 20th July 2015
Ilya Volkovich

#### A Guide to Learning Arithmetic Circuits

An \emph{arithmetic circuit} is a directed acyclic graph in which the operations are $\{+,\times\}$.
In this paper, we exhibit several connections between learning algorithms for arithmetic circuits and other problems.
In particular, we show that:

\begin{enumerate}
\item Efficient learning algorithms for arithmetic circuit classes imply explicit exponential lower bounds.

... more >>>

TR15-134 | 19th August 2015
Fu Li, Iddo Tzameret, Zhengyu Wang

#### Characterizing Propositional Proofs as Non-Commutative Formulas

Does every Boolean tautology have a short propositional-calculus proof? Here, a propositional-calculus (i.e., Frege) proof is any proof starting from a set of axioms and deriving new Boolean formulas using a fixed set of sound derivation rules. Establishing any super-polynomial size lower bound on Frege proofs (in terms of the ... more >>>

TR15-145 | 5th September 2015
Eric Allender, Asa Goodwillie

#### Arithmetic circuit classes over Zm

We continue the study of the complexity classes VP(Zm) and LambdaP(Zm) which was initiated in [AGM15]. We distinguish between “strict” and “lax” versions of these classes and prove some new equalities and inclusions between these arithmetic circuit classes and various subclasses of ACC^1.

more >>>

TR15-154 | 22nd September 2015
Neeraj Kayal, Vineet Nair, Chandan Saha

#### Separation between Read-once Oblivious Algebraic Branching Programs (ROABPs) and Multilinear Depth Three Circuits

We show an exponential separation between two well-studied models of algebraic computation, namely read-once oblivious algebraic branching programs (ROABPs) and multilinear depth three circuits. In particular we show the following:

1. There exists an explicit $n$-variate polynomial computable by linear sized multilinear depth three circuits (with only two product gates) ... more >>>

TR15-181 | 13th November 2015
Neeraj Kayal, Chandan Saha, Sébastien Tavenas

#### On the size of homogeneous and of depth four formulas with low individual degree

Let $r \geq 1$ be an integer. Let us call a polynomial $f(x_1, x_2,\ldots, x_N) \in \mathbb{F}[\mathbf{x}]$ as a multi-$r$-ic polynomial if the degree of $f$ with respect to any variable is at most $r$ (this generalizes the notion of multilinear polynomials). We investigate arithmetic circuits in which the output ... more >>>

TR15-194 | 30th November 2015
Mrinal Kumar, Shubhangi Saraf

#### Arithmetic circuits with locally low algebraic rank

Revisions: 1

In recent years there has been a flurry of activity proving lower bounds for
homogeneous depth-4 arithmetic circuits [GKKS13, FLMS14, KLSS14, KS14c], which has brought us very close to statements that are known to imply VP $\neq$ VNP. It is a big question to go beyond homogeneity, and in ... more >>>

TR15-201 | 10th December 2015
C Ramya, Raghavendra Rao B V

#### Limitations of sum of products of Read-Once Polynomials

Revisions: 1

We study limitations of polynomials computed by depth two circuits built over read-once polynomials (ROPs) and depth three syntactically multi-linear formulas.
We prove an exponential lower bound for the size of the $\Sigma\Pi^{[N^{1/30}]}$ arithmetic circuits built over syntactically multi-linear $\Sigma\Pi\Sigma^{[N^{8/15}]}$ arithmetic circuits computing a product of variable ... more >>>

TR15-202 | 11th December 2015
Meena Mahajan, Raghavendra Rao B V, Karteek Sreenivasaiah

#### Building above read-once polynomials: identity testing and hardness of representation

Polynomial Identity Testing (PIT) algorithms have focused on
polynomials computed either by small alternation-depth arithmetic circuits, or by read-restricted
formulas (ROFs) and are the simplest of read-restricted polynomials.
Building structures above these, we show the following:
\begin{enumerate}
\item A deterministic polynomial-time non-black-box ... more >>>

TR16-006 | 22nd January 2016
Neeraj Kayal, Chandan Saha, Sébastien Tavenas

#### An almost Cubic Lower Bound for Depth Three Arithmetic Circuits

Revisions: 2

We show an $\Omega \left(\frac{n^3}{(\ln n)^2}\right)$ lower bound on the size of any depth three ($\SPS$) arithmetic circuit computing an explicit multilinear polynomial in $n$ variables over any field. This improves upon the previously known quadratic lower bound by Shpilka and Wigderson.

more >>>

TR16-045 | 22nd March 2016
Michael Forbes, Mrinal Kumar, Ramprasad Saptharishi

#### Functional lower bounds for arithmetic circuits and connections to boolean circuit complexity

We say that a circuit $C$ over a field $F$ functionally computes an $n$-variate polynomial $P \in F[x_1, x_2, \ldots, x_n]$ if for every $x \in \{0,1\}^n$ we have that $C(x) = P(x)$. This is in contrast to {syntactically} computing $P$, when $C \equiv P$ as formal polynomials. In this ... more >>>

TR16-096 | 14th June 2016
Suryajith Chillara, Mrinal Kumar, Ramprasad Saptharishi, V Vinay

#### The Chasm at Depth Four, and Tensor Rank : Old results, new insights

Revisions: 2

Agrawal and Vinay [AV08] showed how any polynomial size arithmetic circuit can be thought of as a depth four arithmetic circuit of subexponential size. The resulting circuit size in this simulation was more carefully analyzed by Korian [Koiran] and subsequently by Tavenas [Tav13]. We provide a simple proof of this ... more >>>

TR16-143 | 15th September 2016
Nikhil Balaji, Nutan Limaye, Srikanth Srinivasan

#### An Almost Cubic Lower Bound for $\Sigma\Pi\Sigma$ Circuits Computing a Polynomial in VP

In this note, we prove that there is an explicit polynomial in VP such that any $\Sigma\Pi\Sigma$ arithmetic circuit computing it must have size at least $n^{3-o(1)}$. Up to $n^{o(1)}$ factors, this strengthens a recent result of Kayal, Saha and Tavenas (ICALP 2016) which gives a polynomial in VNP with ... more >>>

TR17-086 | 9th May 2017
C Ramya, Raghavendra Rao B V

#### Linear Projections of the Vandermonde Polynomial

Revisions: 1

An n-variate Vandermonde polynomial is the determinant of the n × n matrix where the ith column is the vector (1, x_i , x_i^2 , . . . , x_i^{n-1})^T. Vandermonde polynomials play a crucial role in the in the theory of alternating polynomials and occur in Lagrangian polynomial interpolation ... more >>>

TR17-124 | 6th August 2017
Mrinal Kumar, Ben Lee Volk

#### An Almost Quadratic Lower Bound for Syntactically Multilinear Arithmetic Circuits

Revisions: 2

We prove a lower bound of $\Omega(n^2/\log^2 n)$ on the size of any syntactically multilinear arithmetic circuit computing some explicit multilinear polynomial $f(x_1, \ldots, x_n)$. Our approach expands and improves upon a result of Raz, Shpilka and Yehudayoff [RSY08], who proved a lower bound of $\Omega(n^{4/3}/\log^2 n)$ for the same ... more >>>

TR18-038 | 21st February 2018
Nathanael Fijalkow, Guillaume Lagarde, Pierre Ohlmann

#### Tight Bounds using Hankel Matrix for Arithmetic Circuits with Unique Parse Trees

This paper studies lower bounds for arithmetic circuits computing (non-commutative) polynomials. Our conceptual contribution is an exact correspondence between circuits and weighted automata: algebraic branching programs are captured by weighted automata over words, and circuits with unique parse trees by weighted automata over trees.

The key notion for understanding the ... more >>>

TR19-104 | 6th August 2019
Vishwas Bhargava, Shubhangi Saraf, Ilya Volkovich

#### Reconstruction of Depth-$4$ Multilinear Circuits

We present a deterministic algorithm for reconstructing multilinear $\Sigma\Pi\Sigma\Pi(k)$ circuits, i.e. multilinear depth-$4$ circuits with fan-in $k$ at the top $+$ gate. For any fixed $k$, given black-box access to a polynomial $f \in \mathbb{F}[x_{1},x_{2},\ldots ,x_{n}]$ computable by a multilinear $\Sigma\Pi\Sigma\Pi(k)$ circuit of size $s$, the algorithm runs in time ... more >>>

ISSN 1433-8092 | Imprint


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### Abstract

As a result of the Kyoto Protocol (KP) and its so-called "flexibility mechanisms", climate change and mechanisms to mitigate its potential effects have attracted considerable economic and policy attention. A major reason for this attention is that the KP has a complex set of instruments that enable countries to achieve emissions reduction targets in a wide variety of ways, some of which are unlikely to lead to real, long-term reductions in greenhouse gas emissions. One purpose of this chapter, therefore, is to provide an overview of economic reasoning applied to climate change and to illustrate how terrestrial carbon uptake credits (offset credits) operate within the KP framework. Attention is focused on the feasibility of terrestrial carbon sinks to slow the rate of CO2 buildup in the atmosphere (Beattie, Bond and Manning 1981). I also examine the results of several empirical studies into the costs of carbon uptake in agricultural ecosystems and by forestry activities. For example, Manley et al. (2004) examined the costs of creating soil carbon sinks by switching from conventional to zero tillage. The viability of agricultural carbon sinks was found to vary by region and crop, with no-till representing a low-cost option in some regions (costs of less than $10/tC), but a high-cost option in others (costs of$100-\$400/tC). A particularly relevant finding is that no-till cultivation may store no carbon at all if measurements are taken at sufficient depth. In some circumstances no-till cultivation may yield a "triple dividend" of carbon storage, increased returns and reduced soil erosion, but in many others creating carbon offset credits in agricultural soils is not cost effective because reduced tillage 1 Prepared for Climate Change and Managed Ecosystems edited by J.S. Bhatti, R. Lal, M. Apps and M. Price. Baton Roca, FL: CRC Press. 2 practices store little or no carbon. This is particularly the case in the Great Plains. In another study, van Kooten (2004) review estimates from 55 studies of the costs of creating carbon offsets using forestry. Lowest costs of sequestering carbon are through forest conservation, while tree planting and agroforestry activities increase costs by more than 200%. The use of marginal cost estimates instead of average cost results in much higher costs for carbon sequestration, in the range of thousands of dollars per tC, although few studies used this more-appropriate method of cost assessment. I conclude by making the case that, while there remains a great potential for carbon sinks, more attention needs to be paid to post-harvest. In the above research, post harvest storage of carbon in wood products yielded much lower cost estimates. Yet, the study of post harvest uses of biomass remains an area that requires greater attention by economists.


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# Recent questions tagged opposite

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Home > Mean Square > Root Mean Square Error Difference

# Root Mean Square Error Difference

## Contents

What is the name for the spoiler above the cabin of a semi? Predictor If Y ^ {\displaystyle {\hat Transclusion expansion time report (%,ms,calls,template) 100.00% 115.650 1 - -total 59.66% 68.997 2 - Template:Reflist 45.08% 52.133 5 - Template:Cite_book 21.46% 24.822 1 - Template:Distinguish-redirect So my question - in what instance would the Root Mean Squared Error be a more appropriate measure of error than the Mean Absolute Error? Applications Minimizing MSE is a key criterion in selecting estimators: see minimum mean-square error. http://objectifiers.com/mean-square/root-mean-square-error-r2.html

That is probably the most easily interpreted statistic, since it has the same units as the quantity plotted on the vertical axis. These individual differences are called residuals when the calculations are performed over the data sample that was used for estimation, and are called prediction errors when computed out-of-sample. McGraw-Hill. The RMSD serves to aggregate the magnitudes of the errors in predictions for various times into a single measure of predictive power.

## Root Mean Square Error Formula

Browse other questions tagged standard-deviation bias or ask your own question. Then work as in the normal distribution, converting to standard units and eventually using the table on page 105 of the appendix if necessary. Probability and Statistics (2nd ed.). Retrieved from "https://en.wikipedia.org/w/index.php?title=Mean_squared_error&oldid=750249597" Categories: Point estimation performanceStatistical deviation and dispersionLoss functionsLeast squares Navigation menu Personal tools Not logged inTalkContributionsCreate accountLog in Namespaces Article Talk Variants Views Read Edit View history More

CS1 maint: Multiple names: authors list (link) ^ "Coastal Inlets Research Program (CIRP) Wiki - Statistics". Further, while the corrected sample variance is the best unbiased estimator (minimum mean square error among unbiased estimators) of variance for Gaussian distributions, if the distribution is not Gaussian then even But what error are you interested in, precisely? Mean Square Error Example So a squared distance from the arrow to the target is the square of the distance from the arrow to the aim point and the square of the distance between the

Text is available under the Creative Commons Attribution-ShareAlike License; additional terms may apply. The (R)MSE is minimized by the conditional mean, the MAE by the conditional median. errors of the predicted values. In statistical modelling the MSE, representing the difference between the actual observations and the observation values predicted by the model, is used to determine the extent to which the model fits

share|improve this answer answered Mar 5 '13 at 14:56 e_serrano 111 add a comment| up vote 0 down vote RMSE is a way of measuring how good our predictive model is Root Mean Square Error In R International Journal of Forecasting. 8 (1): 69–80. The usual estimator for the mean is the sample average X ¯ = 1 n ∑ i = 1 n X i {\displaystyle {\overline {X}}={\frac {1}{n}}\sum _{i=1}^{n}X_{i}} which has an expected Thinking of a right triangle where the square of the hypotenuse is the sum of the sqaures of the two sides.

## Root Mean Square Error Interpretation

Loss function Squared error loss is one of the most widely used loss functions in statistics, though its widespread use stems more from mathematical convenience than considerations of actual loss in Learn more MATLAB and Simulink resources for Arduino, LEGO, and Raspberry Pi Learn more Discover what MATLAB® can do for your career. Root Mean Square Error Formula error). Root Mean Square Error Excel What Am I?

How can I rotate an object based on another's offset to it? References ^ a b Lehmann, E. What would be the predicted value? Check This Out C V ( R M S D ) = R M S D y ¯ {\displaystyle \mathrm {CV(RMSD)} ={\frac {\mathrm {RMSD} }{\bar {y}}}} Applications In meteorology, to see how effectively a

Contents 1 Definition and basic properties 1.1 Predictor 1.2 Estimator 1.2.1 Proof of variance and bias relationship 2 Regression 3 Examples 3.1 Mean 3.2 Variance 3.3 Gaussian distribution 4 Interpretation 5 Normalized Root Mean Square Error The two should be similar for a reasonable fit. **using the number of points - 2 rather than just the number of points is required to account for the fact that United States Patents Trademarks Privacy Policy Preventing Piracy Terms of Use © 1994-2016 The MathWorks, Inc.

## Join them; it only takes a minute: Sign up Here's how it works: Anybody can ask a question Anybody can answer The best answers are voted up and rise to the

The MSE is the second moment (about the origin) of the error, and thus incorporates both the variance of the estimator and its bias. If you optimize the MAE, you may be surprised to find that the MAE-optimal forecast is a flat zero forecast. Next: Regression Line Up: Regression Previous: Regression Effect and Regression   Index Susan Holmes 2000-11-28 Host Competitions Datasets Kernels Jobs Community ▾ User Rankings Forum Blog Wiki Sign up Login Log What Is A Good Rmse Ultimately i want to predict parameters that best suit the data, and e.g. 9% error sound better than 12% - i just wanted to make sure i'm picking the right one

Theory of Point Estimation (2nd ed.). What does "put on one's hat" mean? Compared to the similar Mean Absolute Error, RMSE amplifies and severely punishes large errors. $$\textrm{RMSE} = \sqrt{\frac{1}{n} \sum_{i=1}^{n} (y_i - \hat{y}_i)^2}$$ **MATLAB code:** RMSE = sqrt(mean((y-y_pred).^2)); **R code:** RMSE http://objectifiers.com/mean-square/root-mean-square-error-using-r.html Why my home PC wallpaper updates to my office wallpaper Largest palindrome from given string How to reapply symmetry in sculpting?

error will be 0. However, one can use other estimators for σ 2 {\displaystyle \sigma ^{2}} which are proportional to S n − 1 2 {\displaystyle S_{n-1}^{2}} , and an appropriate choice can always give Definition of an MSE differs according to whether one is describing an estimator or a predictor. The root-mean-square deviation (RMSD) or root-mean-square error (RMSE) is a frequently used measure of the differences between values (sample and population values) predicted by a model or an estimator and the

RMSD is a good measure of accuracy, but only to compare forecasting errors of different models for a particular variable and not between variables, as it is scale-dependent.[1] Contents 1 Formula In computational neuroscience, the RMSD is used to assess how well a system learns a given model.[6] In Protein nuclear magnetic resonance spectroscopy, the RMSD is used as a measure to MR0804611. ^ Sergio Bermejo, Joan Cabestany (2001) "Oriented principal component analysis for large margin classifiers", Neural Networks, 14 (10), 1447–1461. Mean squared error is the negative of the expected value of one specific utility function, the quadratic utility function, which may not be the appropriate utility function to use under a

New York: Springer. MAE will never be higher than RMSE because of the way they are calculated. I am sure many elementary statistics books cover this including my book "The Essentials of Biostatistics for Physicians, Nurses and Clinicians." Think of a target with a bulls-eye in the middle. To use the normal approximation in a vertical slice, consider the points in the slice to be a new group of Y's.

The root-mean-square deviation (RMSD) or root-mean-square error (RMSE) is a frequently used measure of the differences between values (sample and population values) predicted by a model or an estimator and the The RMSD of predicted values y ^ t {\displaystyle {\hat {y}}_{t}} for times t of a regression's dependent variable y t {\displaystyle y_{t}} is computed for n different predictions as the What additional information does the MBD give when considered with the RMSE? For example, if all the points lie exactly on a line with positive slope, then r will be 1, and the r.m.s.

In many cases, especially for smaller samples, the sample range is likely to be affected by the size of sample which would hamper comparisons. In GIS, the RMSD is one measure used to assess the accuracy of spatial analysis and remote sensing. Thus the RMS error is measured on the same scale, with the same units as . Is there any rational, other than MAE being preferable, for using one measure of error over the other?

Though there is no consistent means of normalization in the literature, common choices are the mean or the range (defined as the maximum value minus the minimum value) of the measured Reality would be (Root of MSE)/n.


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DMPG '15 S3 - Zen Garden

View as PDF

Points: 8 (partial)
Time limit: 2.0s
Memory limit: 64M

Author:
Problem type

Zen gardens are intended to serve as an intimate imitation of nature as to aid in meditation about the true meaning of life. Therefore, Blake has decided to spend her summer building one in her backyard.

Each flower has a harmony value, and so she's planted flowers in a row as to ensure a peaceful garden. However, she's discovered that pairs of flowers, when planted beside each other, cause a decrease in the overall harmony of the garden.

The total harmony value of a Zen garden is given by the sum of all flower harmony values minus the sum of all disturbance values. As she wants her garden to have the maximum harmony, she can remove flowers as to eliminate the disturbance they cause.

What is the maximum overall harmony value that Blake can hope to get out of her garden?

Input Specification

The first line of input will consist of the single integer .

The second line will consist of space-separated integers representing the meditation values (between and ) of flowers to as they are planted in Blake's garden.

The next line will consist of the single integer .

The next lines will each consist of two space-separated integers, and , , representing that flower and together cause a decrease in the overall harmony by . Removing either or will remove the disturbance .

It is guaranteed that all flowers will at most be part of one pair.

Output Specification

Output the maximum possible overall meditation value of the garden.

Sample Input

4
5 10 15 20
2
1 30
3 4

Sample Output

41

Explanation of Sample Input

After removing the first flower, the sum of the first two flowers is , as the garden no longer incurs the penalty of . For flowers and , the best choice is to leave them alone, as the penalty of is negligible. Adding these, we obtain the desired output.

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Public Group

# No Default Constructor

This topic is 3629 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic.

## Recommended Posts

In the following code:
AnimatedTile::AnimatedTile(Animation animation);
I'm getting the error: "Animation - no appropriate default constructor available." There is no default constructor for Animation (at least not written by me). I don't want there to be one, because you shouldn't be able to make an Animation without at least one Image in it. Do I not have that option? And why would this error appear here, anyway? An already-constructed Animation should be passed in to this constructor, so if the problem is going to occur, it shouldn't occur here anyway, right? On an unrelated note, how do I make a global constant in a multi-file project? I've tried just const int TILE_SIZE = 32; at the top of main.cpp, but no other file seems able to find it, and I'm trying to avoid just typing 32 every time. Thanks for helping...

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That may be enough code to tell you what your problem is, but I'm not smart enough. At least show all constructors you have for Animation. I'm guessing you need a copy constructor.
Animation::Animation(const Animation &animation){  this->member1 = animation.member1;  // etc...  // or overload operator= and use it here like this:  // *this = animation;}

Problem 2:

Read this a few times. Basically, you'll need to add to make a header file and include that in every file that needs that value. Don't want to do that? Pick a different language. That said, I bet if you wrote your program a little different you would only need to use that constant in one or two files.

Hope that helps.

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Any call to the AnimatedTile constructor is going to invoke the copy constructor for the Animation parameter. This is because you are passing this argument by value. I assume this is not what you want.

If you do not want anyone (including yourself) to use any of the default methods then declare them private.

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I have defined both a copy constructor and an assignment operator for class Animation, as follows:

Animation& Animation::operator =(const Animation& rv){	this->m_Images = rv.m_Images;	this->m_CurrentImage = rv.m_CurrentImage;	this->m_CurrentIndex = rv.m_CurrentIndex;	this->m_Delay = rv.m_Delay;	this->m_Pos = rv.m_Pos;	this->m_Waited = rv.m_Waited;	return *this;}Animation::Animation(const Animation &animation){	*this = animation;}

There is only one constructor for class Animation:

Animation::Animation(std::vector<Image> images, double delay){	m_Images = images;	m_Delay = delay;	m_Waited = 0.0;	m_CurrentImage = m_Images.at(0);	m_CurrentIndex = 0;}

I changed the argument to AnimatedTile's constructor to const Animation& animation, with no change in the error message.

I feel that there's some fundamental gaps in my knowledge of this particular subject... can anyone recommend some research material to me? I didn't see anything promising in the articles section. Books would be fine - I have a very excellent library two blocks from me - but online would be easier.

And just so we're clear - I'd still like to know how to solve the immediate problem, as well as the theory behind why it's happening.

Thanks for the help thus far.

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Did you make your Animation constructor explicit?

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I'm not sure what that means... I've posted the constructor, which is the only one that exists... Its definition in the class header file goes like this:

class Animation{...public:Animation(std::vector<Image> images, double delay);...}

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AnimatedTile::AnimatedTile(Animation animation);

That line of code is very bizarre, actually. What do you think it does?

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Quote:
 Original post by nobodynewsAnimatedTile::AnimatedTile(Animation animation);That line of code is very bizarre, actually. What do you think it does?

Um... It's the declaration (well actually definition, I snipped the body) of a constructor for class AnimatedTile which takes an Animation (which is referred to in said snipped body as animation) as an argument.

... Right?

I'll bet $20 and a chocolate bar that you're doing something like thi in the AnimatedTile class: class AnimatedTile{ Animation anim;public: AnimatedTile(Animation anim) { this -> anim = anim; }} This cannot work, because Animation has no default constructor, and therefore, you have to provide constructor arguments for your AnimatedTile::anim member in the AnimatedTile constructor. This is done using an initializer list: AnimatedTile(Animation anim) : anim(anim) {} #### Share this post ##### Link to post ##### Share on other sites *Gives 20$ and a chocolate bar to ToohrVyk, then hangs his head in shame.*

That, of course, was the problem. Thanks very much for all your help, everyone, and hopefully I'll never do this again...

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Rosa Winter

MPI Leipzig

## Time:

Thursday, February 25, 2021 - 10:00am to 11:00am

## Location:

Zoom: https://uci.zoom.us/j/94683355687
Del Pezzo surfaces are surfaces that are classified by their degree $d$, which is an integer between 1 and 9; well-known examples (when $d=3$) are the smooth cubic surfaces in $\mathbb{P}^3$. For del Pezzo surfaces with $d\geq2$ over a field $k$, we know that the set of $k$-rational points is Zariski dense provided that the surface has one $k$-rational point to start with (that lies outside a specific subset of the surface for degree 2). However, for del Pezzo surfaces of degree 1 we do not know if the set of $k$-rational points is Zariski dense in general, even though these surfaces always contain a $k$-rational point. This makes del Pezzo surfaces of degree 1 challenging objects. In this talk I will first explain what del Pezzo surfaces are, and show some of their geometric features, focussing on del Pezzo surfaces of degree 1. I will then talk about a result that is joint work with Julie Desjardins, in which we give necessary and sufficient conditions for the set of $k$-rational points on a specific family of del Pezzo surfaces of degree 1 to be Zariski dense, where $k$ is any field that is finitely generated over $\mathbb{Q}$.


text:
Re: [NTG-context] Use figures without file extension

On Sun, 27 May 2012, Rogers, Michael K wrote:

I don't know if this helps but the following tells what the type of the image file is. (In my case I copied a jpg to img1 and a png to img2, without extensions of course.)

Thanks.

Hans implemented a version of unix file command for checking the type of images, but using the inbuilt library is definely simpler!

\startluacode
userdata = userdata or { }
function userdata.mytype(s)
context(img.scan({filename=s}).imagetype)
end
\stopluacode

@Hans, btw I also noticed that \locfilename does not work for files without extension. Create a file "one" in the current directory and then run:

\message{>>>\locfilename{one}<<<}
\end


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# Traversal of a 3D Triangle Plane

This topic is 3332 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic.

## Recommended Posts

Hi guys, I am stuck! Traversing terrain in old 2d games was easy. The old straight-line formula worked wonders, with a unit following the line. How would one go about traversing a 3D Triangle terrain?? I have my exact starting point (xs,ys,zs) on the terrain and the exact destination point (xd,yd,zd). Don't know if you require any more information on the problem? Any ideas or a shove to the right algortihm would be appreciated! Best regards, Riaan.

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Let's look at a simple technique for moving around on a terrain made of triangles. If there is some direction that is defined as generally "down" (e.g., the direction gravity would act), and if you have some AI or user control that indicates the desire direction of movement (say, walking), then a conceptually easy way to move around is:

1) Assume +Z is up2) Assume desired movement direction is dir(x,y) ---- given by AI or player control. Must be a unit-length vector.3) Current position is pos(x,y,z)4) Given a movement speed, compute the new (x,y) location:   pos = pos + speed*dir*time_step;   Here, time_step is the amount of time since the last update. For example,   this could be the frame time. Make sure units are consistent, e.g., if   you represent speed in meters/second, then the time step should be in   seconds so that speed * time_step is in meters.5) Ray trace the terrain triangle list using a vertical ray to find   the terrain height:   ray_start_pt = vec(pos.x, pos.y, pos.z + 5.0);   ray_dir = vec(0.0, 0.0, -1.0); // look down towards terrain   terrain_height = ray_trace_terrain_triangles(ray_start_pt, ray_dir);6) Assign terrain height to new pos:   pos.z = terrain_height7) repeat 1-6 for every frame

Here, the first 4 steps really represent 2D movement, in the xy plane, horizontally.

The 5th/6th steps do the terrain following. Here it is very, very simple...just lookup the terrain height by ray tracing using a vertical ray, then assign the found terrain height to the position....the player or object will snap to the terrain.

The reason for the "+ 5.0" in step 5 is so that the ray trace will be slightly above the terrain even if the terrain in the movement direction is going up a hill. This basically enables the object to move up a hill, walk up stairs/steps, follow rocks, etc., that might be represented in the terrain. If you don't include this, and you try to walk up a hill, you will either walk into the terrain instead of on top, or you will fall through, or you will simply disallow movement in any direction where the ray trace does not intersect the terrain.

This isn't a foolproof system. It's very simple. It works, and is easy to code.

The hardest part of this is the ray tracing. It is easy, and you should be able to find posts here (many many posts in the archive) on finding the intersection of a line and a triangle. That's the basic ray tracing algorithm. But to do a fast ray trace against many triangles...the trick here is that you need to do spatial partitioning, and that is what you search should help you with. A spatial partitioning scheme that works well for triangle models is called the Kd-tree. "Ray tracing using a Kd-tree" would probably be a good search phrase.

You can go more complex from here, e.g., adjust speed based on some physical properties of the terrain and object (harder to walk up muddy hill), etc.

I know that was a ramble. I hope it helps.

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Thank you Graham!

I will implement it like this and get back to you if I run into problems.

Best regards,
Riaan.

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Hi Graham,

I have not implemented your algorithm, but have thought it through thoroughly. I think there is a pitfall. Allow me to explain, and please shred my argument if it is not sound.

You said "Here, the first 4 steps really represent 2D movement, in the xy plane, horizontally.", and this is my problem.

Imagine you have a terrain grid with each increment in the X and Y direction being 1. But some rectangles are raised with Z to, say, 4.

If you traverse with this algorithm, the heightened "stretched" triangles will be traversed 'quicker' (the triangle is longer, but its X,Y is the same as other triangles), because the Z is ignored during movement, and Z traced as an afterthought.

Is this wrong??

Riaan.

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Hi guys,

Let me clarify my last post with an image: Worth a thousand words I guess ;)

<br/>

As you can see from the image, the triangle circled in Green and the one circled in Red, have exactly the same dimensions in the XY plane, but, the Green triangle has two of its Vertices lifted (in the Zdirection) relatively high.

Now, if you traverse this terrain in only the XY plane (and pick the value of Z later on), and these two triangles are the same size in XY, then you would traverse both triangles equally fast (time wise). In other words, the larger rectangle will be traversed "quicker" (a larger distance will be covered on the large rectangle in the same time that a smaller distance was covered on the smaller rectangle [blue dotted line]).

Does this make sense to anyone else, or am I missing something?

If my argument is correct, how can I traverse the terrain in 3 dimensions, not only in XY and pick Z later??

Best regards,
Riaan.

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You're absolutely correct, given the same X and Y values, different terrain heights will produce different Z values which will increase or decrease the speed of the traversal. The trick is to normalize the vector [X,Y,Z], which makes it unit length, and then multiply it by your desired travel speed. This way you always cancel out the length variation created by sampling different Z values from the height-map.

However, there's still the issue of moving across triangle boundaries. For instance, if XY is 10 units long, but each terrain cell is only 1x1, then you will pass through multiple triangles in the middle. Unless you take into account all the triangles in-between, your can possibly move through the terrain itself, for instance if you skipped a tall mountain without detecting it. In cases like this you'd have to actually trace the XY vector across the terrain, detect all the triangles it intersects, clip it along those boundaries, and then have multiple traversals that accurately follows the surface of the terrain.

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Quote:
 Original post by ZipsterIn cases like this you'd have to actually trace the XY vector across the terrain, detect all the triangles it intersects, clip it along those boundaries, and then have multiple traversals that accurately follows the surface of the terrain.

I thought about doing this, but how do I detect where the taversal line leaves the current triangle?

I have the current position and the destination, so I have a line to work with. As well as the current triangle's dimensions and all angles inside the triangle. But how do I get the line exit point from here?

Soz, my maths is a bit shoddy.

Riaan.

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Good discussion! I'm on travel, with slow Internet access and a million things to do, so my reply will be brief.

As Riaan observed, the simple approach I presented is based on the idea that the speed of motion is the xy component only, regardless of terrain shape, which will effectively mean the agent/player will accelerate or decelerate depending on the slope of the triangles being traversed.

To be strictly correct about maintaining a constant 3D speed, the piecewise traversal of each triangle crossed in a time step seems necessary; however, a simple compromise might be suitable:

1) Compute the new position based on my algorithm, based on speed being a horizontal constant speed.

2) With the new Z value at the position computed above, you will have a vector from the old 3D position to the new

3) As Zipster suggested, normalize this vector...and assume it'll be your *actual* direction of motion

4) Multiple the result of step 3 times your speed...this'll give you a 3D position that is adjusted for an approximate slope variation between the start and end points.

5) Do a second ray trace to find the actual terrain height, given the adjusted (x,y) coordinate from step 4, and take the step 4 (x,y) + this updated Z to be your final position.

I didn't say that very elegantly. This too isn't perfect, in the way a full piecewise movement across multiple triangles would be. But for time steps that aren't too large and for terrain that doesn't have high frequency variations in height, it might get you close enough to true constant speed to be acceptable. And it'd be less expensive than the full piecewise movement implementation.

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That wasn't brief, was it? ;)

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Haha,

This is getting much closer to what I think I need (might even be exactly what I need!)

Coding it today, and will post the success of the algorithm.

Best regards and thank you for the help.
Riaan.

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text:
Intergrate Calc dont you love it

• Mar 3rd 2008, 06:34 PM
Bust2000
Intergrate Calc dont you love it
Intergrate (2x^2+4x+22) / (x^2+2x+10) dx
• Mar 3rd 2008, 06:58 PM
Soroban
Hello, Bust20001

Quote:

$\int\frac{2x^2+4x+22}{x^2+2x+10}\,dx$

Divide: . $\int\left(2 + \frac{2}{x^2 +2x+10}\right)\,dx$

. . . . . $=\;\;\int\left(2 + \frac{2}{(x+1)^2+9}\right)\,dx$

. . . . . $= \;\;2x + \frac{2}{3}\arctan\left(\frac{x+1}{3}\right)+ C$

• Mar 3rd 2008, 06:58 PM
mr fantastic
Quote:

Originally Posted by Bust2000
Intergrate (2x^2+4x+22) / (x^2+2x+10) dx

$\frac{2x^2 + 4x + 22}{x^2 + 2x + 10} = 2\left( \frac{x^2 + 2x + 11}{x^2 + 2x + 10} \right) = 2\left( \frac{(x^2 + 2x + 10) + 1}{x^2 + 2x + 10} \right)$

$= 2\left( 1 + \frac{1}{x^2 + 2x + 10} \right) = 2\left( 1 + \frac{1}{(x + 1)^2 + 9} \right) = \left( 1 + \frac{1}{3} \, \frac{3}{(x + 1)^2 + 3^2} \right)$.

You should have better luck with this form .....
• Mar 3rd 2008, 07:09 PM
roy_zhang
Quote:

Originally Posted by Bust2000
Intergrate (2x^2+4x+22) / (x^2+2x+10) dx

When your integrand is in the form $\frac{P(x)}{Q(x)}$, where $P(x),Q(x)$ are both polynomials, and the order of $P(x)$ is greater or equal to the order of $Q(x)$; always try long division first before integrating.

Here we have:
$\frac{2x^2+4x+22}{x^2+2x+10} = 2+\frac{2}{x^2+2x+10}$

Now,
$\int\frac{2x^2+4x+22}{x^2+2x+10}dx = \int (2+\frac{2}{x^2+2x+10})dx = \int2dx + \int[\frac{2}{(x+1)^2+3^2}]dx$

use $u$ substitution (let $u= x+1$)

we got:

$\int \frac{2x^2+4x+22}{x^2+2x+10}dx=2x + \frac{2}{3}\arctan(\frac{x+1}{3}) + C$


text:
# How to resize an image loaded using ContentManager in XNA

I am new to XNA programming and I loaded the background image using ContentManager as a Texture2D object.

The background image which I have is of size 480*320. I have kept the minimum game window size as 640*480. My question is how would i resize the background image to the size of the game window.

SpriteBatch.Draw(background_texture, GraphicsDevice.Viewport.Bounds, Color.White);


text:
Dataplot Vol 1 Vol 2

# RANK SUM TEST

Name:
RANK SUM TEST
Type:
Analysis Command
Purpose:
Perform a two sample rank sum test.
Description:
The t-test is the standard test for testing that the difference between population means for two non-paired samples are equal. If the populations are non-normal, particularly for small samples, then the t-test may not be valid. The rank sum test is an alternative that can be applied when distributional assumptions are suspect. However, it is not as powerful as the t-test when the distributional assumptions are in fact valid.

The rank sum test is also commonly called the Mann-Whitney rank sum test or simply the Mann-Whitney test. Note that even though this test is commonly called the Mann-Whitney test, it was in fact developed by Wilcoxon.

To form the rank sum test, rank the combined samples. Then compute the sum of the ranks for sample one, T1, and the sum of the ranks for sample two, T2. If the sample sizes are equal, the rank sum test statistic is the minimum of T1 and T2. If the sample sizes are unequal, then find T1 equal the sum of the ranks for the smaller sample. Then compute T2 = n1(n1 + n2 + 1) - T1. T is the minimum of T1 and T2. Sufficiently small values of T cause rejection of the null hypothesis that the sample means are equal.

Significance levels have been tabulated for small values of n1 and n2. For sufficiently large n1 and n2, the following normal approximation is used:

$$Z = \frac{|\mu - T| - 0.5} {\sigma}$$

where

$$\mu = n_1(n_1 + n_2 + 1)/2$$

$$\sigma = \sqrt{n_2 \mu /6}$$

Syntax:
RANK SUM TEST <y1> <y2>             <SUBSET/EXCEPT/FOR qualification>
where <y1> is the first response variable;
<y2> is the second response variable;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.
Examples:
RANK SUM TEST Y1 Y2
RANK SUM TEST Y1 Y2 SUBSET TAG > 2
Note:
Dataplot saves the following internal parameters after a rank sum test:

 STATVAL - The rank sum test statistic STATCD2 - the normal cdf value of T (only applies for sufficiently large N1 and N2) CUTLOW90 - 0.05 critical value CUTUPP90 - 0.95 critical value CUTLOW95 - 0.025 critical value CUTUPP95 - 0.975 critical value CUTLOW99 - 0.005 critical value CUTUPP99 - 0.995 critical value

Note that the above critical values are the lower and upper tails for two sided tests (i.e., each tail is alpha/2. For example, CUTLOW90 is the lower 5% of the normal percent point function (adjusted for the mean and standard deviation). This is the critical regions for alpha = 0.10, so there is 0.05 in each tail.

Note:
The following statistics are also supported:

LET A = MANN WHITNEY RANK SUM TEST Y1 Y2
LET A = MANN WHITNEY RANK SUM TEST CDF Y1 Y2
LET A = MANN WHITNEY RANK SUM TEST PVALUE Y1 Y2
LET A = MANN WHITNEY RANK SUM LOWER TAILED PVALUE Y1 Y2
LET A = MANN WHITNEY RANK SUM UPPER TAILED PVALUE Y1 Y2

In addition to the above LET command, built-in statistics are supported for about 20+ different commands (enter HELP STATISTICS for details).

Default:
None
Synonyms:
The following are synonyms for RANK SUM TEST:

MANN WHITNEY RANK SUM TEST
MANN WHITNEY RANK SUM
MANN WHITNEY TEST
MANN WHITNEY
RANK SUM
Related Commands:
 T-TEST = Compute a t-test. SIGN TEST = Compute a sign test. SIGNED RANK TEST = Compute a signed rank test. CHI-SQUARED 2 SAMPLE TEST = Compute a two sample chi-square test. BIHISTOGRAM = Generates a bihistogram. QUANTILE-QUANTILE PLOT = Generate a quantile-quantile plot. BOX PLOT = Generates a box plot.
Reference:
Snedecor and Cochran (1989), "Statistical Methods," Eighth Edition, Iowa State University Press, pp. 142-144.
Applications:
Confirmatory Data Analysis
Implementation Date:
1999/5
Program:

SKIP 25
RETAIN Y2 SUBSET Y2 > -90
SET WRITE DECIMALS 4
RANK SUM TEST Y1 Y2

The following output is generated.
            Two Sample Two-Sided Mann Whitney Rank Sum Test
(Conover Formulation)

First Response Variable: Y1
Second Response Variable: Y2

H0: F(x) = G(x)   for all x
Ha: F(x) <> G(x)  for some x

Summary Statistics:
Number of Observations for Sample 1:     13
Mean for Sample 1:                       80.0208
Median for Sample 1:                     80.0300
Number of Observations for Sample 2:     8
Mean for Sample 2:                       79.9788
Median for Sample 2:                     79.9700
Number of Tied Ranks:                    14

Test (Normal Approximation):
Test Statistic Value (W):                2.7105
CDF Value:                               0.9966
P-Value (2-tailed test):                 0.0067
P-Value (lower-tailed test):             0.9966
P-Value (upper-tailed test):             0.0034

Two-Tailed Test: Normal Approximation

H0: F(x) = G(x); Ha: F(x) <> G(x)  for some x
------------------------------------------------------------
Null
Significance           Test       Critical     Hypothesis
Level      Statistic    Value (+/-)     Conclusion
------------------------------------------------------------
80.0%         2.7105         1.2816         REJECT
90.0%         2.7105         1.6449         REJECT
95.0%         2.7105         1.9600         REJECT
99.0%         2.7105         2.5758         REJECT

NIST is an agency of the U.S. Commerce Department.

Date created: 06/05/2001
Last updated: 11/04/2015


text:
### Adding custom tools to Galaxy

Vast number of good and well-implemented tools for Galaxy is available through the Galaxy ToolShed and you can freely install any of them into your Galaxy instance via the admin interface. Short tutorial to get you started is available here.

If you did not find your favorite tool in the ToolShed you can always add it to your Galaxy manually (and later share in the Tool Shed with the rest of the world if you like). This article will help you with this creation of a custom tool in your Galaxy.

#### 1. Write and test your tool outside Galaxy:

Suppose one has written a simple Perl script (called toolExample.pl) for computing the GC content of a sequence in the FASTA format, which looks like this:

#!/usr/bin/perl -w

# usage : perl toolExample.pl <FASTA file> <output file>

open (IN, "<$ARGV[0]"); open (OUT, ">$ARGV[1]");
while (<IN>) {
chop;
if (m/^>/) {
s/^>//;
if ($. > 1) { print OUT sprintf("%.3f",$gc/$length) . "\n"; }$gc = 0;
$length = 0; } else { ++$gc while m/[gc]/ig;
$length += length$_;
}
}
print OUT sprintf("%.3f", $gc/$length) . "\n";
close( IN );
close( OUT );

To integrate this tool into Galaxy we will follow these steps:

#### 2. Put tool into Galaxy's tools directory:

To begin the tool integration process we need to add our Perl script to the tools/ directory, where all tool-related files are stored. In this example we will create a new subdirectory called myTools within tools/. So cd to your Galaxy installation and type these commands:

cd tools
mkdir myTools
cd myTools

Now one needs to copy the script (in this case toolExample.pl) into the tools/myTools/ directory.

#### 3. Create Tool Definition File:

At this point toolExample.pl resides within the tools/myTools/ directory, but Galaxy still does not know how to run this tool. To let Galaxy know the execution details of our new tool, we need to write a tool configuration file, which, in this case, will be called toolExample.xml. For this particular example open a text editor of your choice and create the toolExample.xml file within the tools/myTools directory. This file looks like this:

<tool id="fa_gc_content_1" name="Compute GC content" version="0.1.0">
<description>for each sequence in a file</description>
<command interpreter="perl">toolExample.pl $input$output</command>
<inputs>
<param format="fasta" name="input" type="data" label="Source file"/>
</inputs>
<outputs>
<data format="tabular" name="output" />
</outputs>

<tests>
<test>
<param name="input" value="fa_gc_content_input.fa"/>
<output name="out_file1" file="fa_gc_content_output.txt"/>
</test>
</tests>

<help>
This tool computes GC content from a FASTA file.
</help>

</tool>

Note how this file specifies command line parameters, links them to input and output, and provides help information using the restructured text format. Once you are done, the tools/myTools directory will contain two files toolExample.pl and toolExample.xml. For basic and general tool definition file please see Example Tool Definiton File. Once you feel comfortable with the basics you can browse through the full tool definition syntax.

#### 4. Make Galaxy aware of the new tool:

Now the tool and its configuration file are ready. The final step makes Galaxy aware of the new tools. Galaxy knows about installed tools (and also what to display on the left pane) from the tool_conf.xml tool-registry file. Thus, letting Galaxy know about our new tool is as easy as adding these lines to the tool_conf.xml file located in the config directory of the Galaxy distribution:

 <section name="MyTools" id="mTools">
<tool file="myTools/toolExample.xml" />
</section>

#### 5. Start it up:

At this point, start Galaxy by typing sh run.sh from within Galaxy's root directory and point your browser to http://localhost:8080. The interface of the new tool will look like this:

Note the correspondence between elements of the toolExample.xml file (Step 2) and the interface elements shown above. The "Compute GC for" dropdown reads "no data has the proper type" because the history pane contains no data in the FASTA format (it is empty).


text:
# Single-slit diffraction

Tags:
1. Dec 14, 2014

### dreaan

In my physics book, one of the basic quick quizzes checkpoints asks what happens to the central peak in a diffraction envelope when you decrease the wavelength of light (from 650 nm to 450 nm, for reference).

My understanding is that the width of the peak would decrease, while the number of interference fringes would remain the same.
This is because the number of interference fringes depends only on the width of the slit and the distance of the screen based on m=d/a.
The width of the peak decreases, because using the equation asin(theta)=m(lambda), m and a are constant, while changing lambda would change theta, thereby changing the height of the central maximum. The first order minimum would be closer to the center with a smaller wavelength.

However, my book says the answer is that the width of the peak remains the same (along with the number of interference fringes).

This seems inherently wrong. Based on my research on the internet, as well as the interactive picture my book included with the question, I feel like the publishers made a mistake in the answer. Clearly, wavelength affects the diffraction pattern. Right? Please help. My brain hurts.

2. Dec 14, 2014

### dreaan

oops, this question is regarding the combined effects of two-slit and single-slit interference, not just single slit. That makes a pretty big difference, but I am still pretty confused. Any help would be appreciate.

3. Dec 14, 2014

### Staff: Mentor

4. Dec 14, 2014

### dreaan

Thanks, Bill. I don't really see two much in there that answers my question. Here is where I am having trouble grasping the supposed easy question in my book. Interference pattern depends on wavelength. Diffraction pattern depends on wavelength. How does the combined effects not depend on wavelength. This seems counter-intuitive.

5. Dec 14, 2014

### dreaan

too*

6. Dec 14, 2014

### Staff: Mentor

You are stuck in the wave-particle paradigm by thinking in terms of wavelength. Forget it. My link gives the correct analysis.

That said, in that paradigm obviously the interference pattern will depend on wavelength so your objection leaves me scratching my head.

Thanks
Bill

7. Dec 14, 2014

### dreaan

I'm sorry, but that article does not make sense to me. This is supposedly a somewhat simple understanding in my introductory quantum physics class.

#### Attached Files:

• ###### diffractionEnvelope.jpg
File size:
53.3 KB
Views:
122
8. Dec 14, 2014

### Staff: Mentor

As far as I can see that's purely a classical wave analysis.

What I am saying is this wave-particle duality stuff is simply a way-station to the correct theory which doesn't really have it. The link I gave is the correct explanation.

But as a wave analysis I cant see anything wrong or what your issue is.

Thanks
Bill

9. Dec 14, 2014

### dreaan

The chapter I am studying primarily has to do with wave analysis. My problem is that based on the information I have learned, with a combination of single-slit and multi-slit pattern, if the wavelength is decreased, the central maximum should also decrease in width. The interference fringes should also decrease in width, although there are the same number of them within the central diffraction envelop. My book asks this question. It says the answer is that everything remains the same. I just don't see how this could be the correct, based on the equations provided.

10. Dec 14, 2014

### dreaan

So if the width of the peak remains constant and the number of fringes remains constant, what WOULD change if the wavelength changes. Surely something has to. I am wondering if there is a mistake in the book.

11. Dec 14, 2014

### Staff: Mentor

I would need to go through the book.

But if the wavelength changes what doesn't change is getting only single particle hits - of course the pattern changes with particle wavelength.

But I want to emphasise this wave-particle duality is a crock. Its not the real explanation.

Thanks
Bill

12. Dec 14, 2014

### dreaan

okay, thank you, I appreciate your help. based on what I have researched online, their answer is incorrect, which is even more frustrating. I will go back and try to comprehend the article you sent me after my final exams.

13. Dec 15, 2014

### vanhees71

The single-slit interference pattern in Fraunhofer observation is described as the Fourier transform of the opening, i.e., the amplitude is given by
$$A(x) \propto \int_{-d/2}^{d/2} \mathrm{d} y \exp(\mathrm{i} k x y/L)=\frac{L}{\mathrm{i} k x}[\exp[\mathrm{i} k x d/(2L)]-\exp[\mathrm{i} k x d/(2L)]]=\frac{2L}{kx} \sin \left (\frac{k x d}{2L} \right ).$$
The width is usually taken as the distance of the first minimum relative to the main maximum at $x=0$, which is thus found by
$\frac{\Delta x k d}{2L}=\pi \; \Rightarrow \; \Delta x=\frac{2 \pi L}{k d}=\frac{\lambda L}{d}.$
This shows that the width is proportional to the wave length $\lambda$ and the distance from the slit to the screen and inversely proportional to the width of the slit (the approximations involved require $\lambda \ll d \ll L$.

For more details, see
http://en.wikipedia.org/wiki/Diffraction#Single-slit_diffraction
and
http://en.wikipedia.org/wiki/Diffraction_formalism

14. Apr 22, 2015

dreaan,


text:
Chapter 7

# Vector Calculus

## 7.1 Scalars and Vectors

### 7.1.1 Introduction

Scalar Quantities. There are two types of quantities describing fluid flows: scalar and vector quantities. Scalar quantities are quantities that are described only by a magnitude. They do not have a direction of action. For fluids the relevant scalar quantities are

temperature T , measured in K

density ρ, measured in kg m− 3

pressure p, measured in Pa

In the following we will use the symbol ψ whenever referring to a scalar quantity.

Vector Quantities. Vector quantities have both magnitude and a direction of action. The relevant vector quantities of fluid flows are

position $\stackrel{\to }{s}$, measured in m

velocity $\stackrel{\to }{v}$, measured in m s 1

acceleration $\stackrel{\to }{a}$, measured in m s 2

In the ...

Get Microfluidics: Modeling, Mechanics and Mathematics now with O’Reilly online learning.

O’Reilly members experience live online training, plus books, videos, and digital content from 200+ publishers.


text:
## Organic Chemistry (8th Edition)

Published by Pearson

# Chapter 3 - Structure and Stereochemistry of Alkanes - Problems - Page 123: Problem 3-28 f

#### Answer

The IUPAC name of the compound is $trans−1,4−dimethylcyclohexane$

#### Work Step by Step

The compound has 6 carbon atoms in the carbon ring ($−hex$). There are 2 methyl groups attached to the ring at positons 1 and 4, both on the oppposite side of the plane relative to the H atoms ($trans$). So, the IUPAC name of the compound is $trans−1,4−dimethylcyclohexane$

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.


text:
# Time-delay differential equation

Is it possible that the system $$\begin{cases} 2\dot{q}(t) + \dot{q}(t-1) + \dot{q}(t+1) = c & \text{if} \hspace{5mm} 0 \le t \le 2 , \dot{q}(t) + \dot{q}(t-1) = k & \text{if} \hspace{5mm} 2 \le t \le 3 \end{cases}$$ has, for suitable constants $c$ and $k$, any $\mathcal{C}^2$ solutions $q:[-1,3] \to \mathbb{R}$ satisfying the conditions $q(t) = - t$ for $t \in [-1, 0]$ and $q(3)=2$ ?

-
Cross-posted at math.stackexchange.com/questions/342677/… –  Joel Reyes Noche Mar 27 '13 at 22:56
@filippo, posting the same question simultaneously on two or more sites is frowned upon because it leads to duplication of effort on the part of the answerers. At the very least, you should provide links to the other sites you posted the question on. –  Joel Reyes Noche Mar 27 '13 at 22:57