text:
.01

PERSONAL DETAILS
Clemson University, Clemson, SC 29631
+1 (864) 656-1657
office: Martin Hall O-22
O-110 Martin Hall, Box 340975, Clemson, SC 29634

### BIO

I am an Associate Professor of the School of Mathematical and Statistical Sciences of Clemson University. For the academic year 2019/20 I have been a Visiting Scholar of the Ted Rogers School of Management of Ryerson University where I joined the Cybersecurity Research Lab.

.02

## RESUME

• 2019
Clemson, USA

### ASSOCIATE PROFESSOR

#### CLEMSON UNIVERSITY

School of mathematical and Statistical Sciences
• 2019
2020

### VISITING SCHOLAR

#### RYERSON  UNIVERSITY

Cybersecurity Lab, TED ROGERS School of Management
• 2013
2019
Clemson, USA

### ASSISTANT PROFESSOR

#### CLEMSON UNIVERSITY

School of mathematical and Statistical Sciences
• 2011
2013

### POSTDOCTORAL FELLOW

#### UNIVERSITY OF TORONTO

Department of Electrical and Computer Engineering
• OTHER AFFILIATIONS
• 2006
2011

### AFFILIATED FACULTY

#### RYERSON UNIVERSITY

Cybersecurity Research Lab (CRL)
• EDUCATION
• 2006
2011
ZURICH, SWITZERLAND

### MATHEMATICS - DR. SC. NAT (PHD)

#### UNIVERSITY OF ZURICH

Title: Spread Codes and more General Network Codes.
• 1999
2005
PISA, ITALY

### MATHEMATICS

#### UNIVERSITY OF PISA

title: Calcolo della distribuzione dei pesi nei codici ciclici accorciati.
.03

## PUBLICATIONS

PUBLICATIONS LIST
2021

### INTERFERENCE ALIGNMENT IN MULTIPLE UNICAST NETWORKS OVER FINITE FIELDS

#### Submitted.

Jornal Paper with F. Kschischang, A. Ravagnani and K. Savary

### INTERFERENCE ALIGNMENT IN MULTIPLE UNICAST NETWORKS OVER FINITE FIELDS

F. Kschischang, F. Manganiello, A. Ravagnani and K. Savary Journal Paper

2021

### RECURSIVE EDGE TOGGLING FOR CONSTRUCTION OF DE BRUIJN SEQUENCES

#### Submitted.

Conference Proceedings with T. Baumbaugh

### RECURSIVE EDGE TOGGLING FOR CONSTRUCTION OF DE BRUIJN SEQUENCES

T. Baumbaugh and F. Manganiello Conference Proceedings

De Bruijn sequences are cyclic sequences of length $2^n$ that contain every binary word of length $n$ exactly once. The construction of many such sequences of a given order is useful for the generation of stream ciphers. One method of constructing sequences makes use of a homomorphism from the de Bruijn graph of order $n$ to the graph of order $n-1$. The preimages of a de Bruijn sequence under this homomorphism form two cycles which may be joined at certain points. We examine a par- ticular method for identifying such points when the sequence in question is recursively constructed in this manner. Using the structure of the con- struction, we are able to calculate sums of subsequences in $\mathcal{O}( n^4 log(n))$􏰁 time, and the location of a given word in $\mathcal{O}(n^5 log(n))$ time. Together, these functions allow a check to be made for the validity of any potential toggle point. This provides a method for efficiently generating a recursive specification for such sequences, each successful step of which takes $\mathcal{O}(k^5 log(k))$, for $k$ from 3 to n.

15 JAN 2021

### A PARALLEL JACOBI-EMBEDDED GAUSS-SEIDEL METHOD.

#### IEEE Transactions on Parallel and Distributed Systems, 32(6):1452–1464.

Find it in the journal.

### A PARALLEL JACOBI-EMBEDDED GAUSS-SEIDEL METHOD.

A. Ahmadi, F. Manganiello, A. Khademi, and M. C. Smith Journal Paper

A broad range of scientific simulations involve solving large-scale computationally expensive linear systems of equations. Iterative solvers are typically preferred over direct methods when it comes to large systems due to their lower memory requirements and shorter execution times. However, selecting the appropriate iterative solver is problem-specific and dependent on the type and symmetry of the coefficient matrix. Gauss-Seidel (GS) is an iterative method for solving linear systems that are either strictly diagonally dominant or symmetric positive definite. This technique is an improved version of Jacobi and typically converges in fewer iterations. However, the sequential nature of this algorithm complicates the parallel extraction. In fact, most parallel derivatives of GS rely on the sparsity pattern of the coefficient matrix and require matrix reordering or domain decomposition. In this article, we introduce a new algorithm that exploits the convergence property of GS and adapts the parallel structure of Jacobi. The proposed method works for both dense and sparse systems and is straightforward to implement. We have examined the performance of our method on multicore and many-core architectures. Experimental results demonstrate the superior performance of the proposed algorithm compared with GS and Jacobi. Additionally, performance comparison with built-in Krylov solvers in MATLAB showed that in terms of time per iteration, Krylov methods perform faster on CPUs, but our approach is significantly better when executed on GPUs. Lastly, we apply our method to solve the power flow problem, and the results indicate a significant improvement in runtime, reaching up to 87 times faster speed compared with GS.

1 OCT 2020

### HILBERT MODULAR FORMS AND CODES OVER ${\bf F}_{p^2}$

#### Finite Fields and Their Applications, 67:101731.

Find it in the journal.

Journal Paper with J. Brown, J. Lilly and B. Gunsolus

### HILBERT MODULAR FORMS AND CODES OVER ${\bf F}_{p^2}$

J. Brown, J. Lilly, B. Gunsolus and F. Manganiello Journal Paper

Let $p$ be an odd prime and consider the finite field $\mathbb{F}_{p^2}$. Given a linear code $\mathcal{C} \subset \mathbb{F}^{n}_{p^2}$, we use algebraic number theory to construct an associated lattice $\Lambda_{\mathcal{C}} \subset \mathcal{O}_{L}^{n}$ for $L$ an algebraic number field and $\mathcal{O}_{L}$ the ring of integers of $L$. We attach a theta series $\theta_{\Lambda_{\mathcal{C}}}$ to the lattice $\Lambda_{\mathcal{C}}$ and prove a relation between $\theta_{\Lambda_{\mathcal{C}}}$ and the complete weight enumerator evaluated on weight one theta series.

25 OCT 2019

### MULTICAST TRIANGULAR SEMILATTICE NETWORK

#### Involve, Vol. 12 (2019), No. 8, 1307–1328

Find it in the journal.

Journal Paper with A. Grosso, S. Varal and E. Zhu

### MULTICAST TRIANGULAR SEMILATTICE NETWORK.s

A. Grosso, F. Manganiello, S. Varal and E. Zhu Journal Paper

We investigate the structure of the code graph of a multicast network that has a characteristic shape of an inverted equilateral triangle. We provide a criterion that determines the validity of a receiver placement within the code graph, present invariance properties of the determinants corresponding to receiver placements under symmetries, and provide a complete study of these networks’ receivers and required field sizes up to a network of 4 sources. We also improve on various definitions related to code graphs.

1 MAY 2019

### AFFINE CARTESIAN CODES WITH COMPLEMENTARY DUALS

#### Finite Fields and Their Applications 57, 13-28

Find it in the journal.

Journal Paper with H. López and G. Matthews

### AFFINE CARTESIAN CODES WITH COMPLEMENTARY DUALS

H. López, F. Manganiello and G. Matthews Journal Paper

A linear code $C$ with the property that $C \cap C^\perp = \{0\}$ is said to be a linear complementary dual, or LCD, code. In this paper, we consider generalized affine Cartesian codes which are LCD. Generalized affine Cartesian codes arise naturally as the duals of affine Cartesian codes in the same way that generalized Reed–Solomon codes arise as duals of Reed–Solomon codes. Generalized affine Cartesian codes are evaluation codes constructed by evaluating multivariate polynomials of bounded degree at points in an m-dimensional Cartesian set over a finite field K and scaling the coordinates. The LCD property depends on the scalars used. Because Reed–Solomon codes are a special case, we obtain a characterization of those generalized Reed–Solomon codes which are LCD along with the more general result for generalized affine Cartesian codes. These results are independent of the characteristic of the underlying field.

25 APR 2019

### MATROIDAL ROOT STRUCTURE OF SKEW POLYNOMIALS OVER FINITE FIELDS

#### Journal of Discrete Mathematical Sciences and Cryptography, 22(3):377–389

Find it in the journal.

Journal Paper with T. Baumbaugh

### MATROIDAL ROOT STRUCTURE OF SKEW POLYNOMIALS OVER FINITE FIELDS

T. Baumbaugh and F. Manganiello Journal Paper

A skew polynomial ring $R=K[x;\sigma,\delta]$ is a ring of polynomials with non-commutative multiplication. This creates a difference between left and right divisibility, evaluations, and roots. A polynomial in such a ring may have more roots than its degree, which leads to the concepts of closures and independent sets of roots. In $R=\mathbb{F}_{q^m}[x;\sigma]$, this leads to the matroids $\mathfrak{M}_r$ and $\mathfrak{M}_l$ of right independent and left independent sets, which are isomorphic via the extension of the map $\phi : [1] \rightarrow [1]$ defined by $\phi(a)=a^{(m)}$, where $( i)=\frac{q^{i-1}-1}{q-1}$. Extending the field of coefficients of R results in a new ring $S$ of which $R$ is a subring, and if the extension is taken to include roots of an evaluation polynomial of $f (x)$, then all roots of $f (x)$ in $S$ are in the same conjugacy class.

8 OCT 2018

### BATCH CODES FROM HAMMING AND REED-MULLER CODES

#### Journal of Algebra Combinatorics Discrete Structures and Applications, 5:153 – 165

Find it in the journal.

Journal Paper with T. Baumbaugh

### BATCH CODES FROM HAMMING AND REED-MULLER CODES

T. Baumbaugh and F. Manganiello Journal Paper

Batch codes, introduced by Ishai et al., encode a string $x\in\sum^k$ into an $m$-tuple of strings, called buckets. In this paper we consider multiset batch codes wherein a set of $t$-users wish to access one bit of information each from the original string. We introduce a concept of optimal batch codes. We first show that binary Hamming codes are optimal batch codes. The main body of this work provides batch properties of Reed-Muller codes. We look at locality and availability properties of first order Reed-Muller codes over any finite field. We then show that binary first order Reed-Muller codes are optimal batch codes when the number of users is 4 and generalize our study to the family of binary Reed-Muller codes which have order less than half their length.

16 NOV 2017

### REPRESENTATIONS OF THE MULTICAST NETWORK PROBLEM

#### in ALGEBRAIC GEOMETRY FOR CODING THEORY AND CRYPTOGRAPHY, pages 1–23. Springer International Publishing

Find it in the book.

Book Chapters with S.E. Anderson, W. Halbawi, N. Kaplan, H.H. López, E. Soljanin, and J.L. Walker.

### REPRESENTATIONS OF THE MULTICAST NETWORK PROBLEM

S.E. Anderson, W. Halbawi, N. Kaplan, H.H. López, F. Manganiello, E. Soljanin, and J.L. Walker. Book Chapters

We approach the problem of linear network coding for multicast networks from different perspectives. We introduce the notion of the coding points of a network, which are edges of the network where messages combine and coding occurs. We give an integer linear program that leads to choices of paths through the network that minimize the number of coding points. We introduce the code graph of a network, a simplified directed graph that maintains the information essential to understanding the coding properties of the network. One of the main problems in network coding is to understand when the capacity of a multicast network is achieved with linear network coding over a finite field of size q. We explain how this problem can be interpreted in terms of rational points on certain algebraic varieties.

10 OCT 2017

### CODES FOR DISTRIBUTED STORAGE FROM 3-REGULAR GRAPHS

#### Discrete Applied Mathematics, 229:82–89

Find it in the journal.

Journal Paper with S. Gao, F. Knoll and G. Matthews

### CODES FOR DISTRIBUTED STORAGE FROM 3-REGULAR GRAPHS

S. Gao, F. Knoll, F. Manganiello and G. Matthews Journal Paper

This paper considers distributed storage systems (DSSs) from a graph theoretic perspective. A DSS is constructed by means of the path decomposition of a 3-regular graph into $P_4$ paths. The paths represent the disks of the DSS and the edges of the graph act as the blocks of storage. We deduce the properties of the DSS from a related graph and show their optimality.

17 MAY 2017

### MATROIDAL STRUCTURE OF SKEW POLYNOMIAL RINGS WITH APPLICATION TO NETWORK CODING

#### Finite Fields and Their Applications, 46:326-346

Find it in the journal.

Journal Paper with S. Liu and F. Kschischang

### MATROIDAL STRUCTURE OF SKEW POLYNOMIAL RINGS WITH APPLICATION TO NETWORK CODING

S. Liu, F. Manganiello and F. Kschischang Journal Paper

Over a finite field $\mathbb{F}_{q^m}$, the evaluation of skew polynomials is intimately related to the evaluation of linearized polynomials. This connection allows one to relate the concept of polynomial independence defined for skew polynomials to the familiar concept of linear independence for vector spaces. This relation allows for the definition of a representable matroid called the $\mathbb{F}_{q^m}[x;\sigma]$-matroid, with rank function that makes it a metric space. Specific submatroids of this matroid are individually bijectively isometric to the projective geometry of $\mathbb{F}_{q^m}$ equipped with the subspace metric. This isometry allows one to use the $\mathbb{F}_{q^m}[x;\sigma]$-matroid in a matroidal network coding application.

6 JUL 2015

### CONSTRUCTION AND DECODING OF GENERALIZED SKEW-EVALUATION CODES

#### In the proceeding of the 2015 IEEE 14th Canadian Workshop on Information Theory (CWIT)

Find it is the proceedings of the workshop.

Conference Proceedings with S. Liu and F. Kschischang

### CONSTRUCTION AND DECODING OF GENERALIZED SKEW-EVALUATION CODES

S. Liu, F. Manganiello and F. Kschischang Conference Proceedings

Skew polynomials are elements of a noncommutative ring that, in recent years, have found applications in coding theory and cryptography. Skew polynomials have a well-defined evaluation map. This map leads to the definition of a class of codes called Generalized Skew-Evaluation codes that contains Gabidulin codes as a special case as well as other related codes with additional desirable properties. A Berlekamp-Welch-type decoder for an important class of these codes can be constructed using Kötter interpolation in skew polynomial rings.

17 SEP 2013

### SPREAD DECODING IN EXTENSION FIELDS

#### Finite Fields and Their Applications, 25(0):94–105

Find it in the journal.

Journal Paper with A.-L. Trautmann-Horlemann

### SPREAD DECODING IN EXTENSION FIELDS

A.-L. Trautmann-Horlemann and F. Manganiello Journal Paper

A spread code is a set of vector spaces of a fixed dimension over a finite field $\mathbb{F}_{q}$ with certain properties used for random network coding. It can be constructed in different ways which lead to different decoding algorithms. In this work we consider one such representation of spread codes and present a minimum distance decoding algorithm which is efficient when the code words, the received space and the error space have small dimension.

1 AUG 2013

### CYCLIC ORBIT CODES

#### IEEE Transactions on Information Theory, 59(11):7386-7404

Find it in the journal.

Journal Paper with M. Braun, J. Rosenthal and A.-L. Trautmann-Horlemann

### CYCLIC ORBIT CODES

A.-L. Trautmann-Horlemann, F. Manganiello, M. Braun and J. Rosenthal Journal Paper

A constant dimension code consists of a set of k-dimensional subspaces of $\mathbb{F}_{q^n}$. Orbit codes are constant dimension codes which are defined as orbits of a subgroup of the general linear group, acting on the set of all subspaces of $\mathbb{F}_{q^n}$. If the acting group is cyclic, the corresponding orbit codes are called cyclic orbit codes. In this paper, we show how orbit codes can be seen as an analog of linear codes in the block coding case. We investigate how the structure of cyclic orbit codes can be utilized to compute the minimum distance and cardinality of a given code and propose different decoding procedures for a particular subclass of cyclic orbit codes.

3 JAN 2013

### KÖTTER INTERPOLATION IN SKEW POLYNOMIAL RINGS

#### Designs, Codes and Cryptography, Volume 72, Issue 3, pp 593–608

Find it in the journal.

Journal Paper with S. Liu and F. Kschischang

### KÖTTER INTERPOLATION IN SKEW POLYNOMIAL RINGS

S. Liu, F. Manganiello and F. Kschischang Journal Paper

Skew polynomials are a noncommutative generalization of ordinary polynomials that, in recent years, have found applications in coding theory and cryptography. Viewed as functions, skew polynomials have a well-defined evaluation map; however, little is known about skew-polynomial interpolation. In this work, we apply Kötter’s interpolation framework to free modules over skew polynomial rings. As a special case, we introduce a simple interpolation algorithm akin to Newton interpolation for ordinary polynomials.

1 NOV 2012

### AN ALGEBRAIC APPROACH FOR DECODING SPREAD CODES

#### Advances in Mathematics of Communications, 6(4):443-466

Find it in the journal.

Journal Paper with E. Gorla and J. Rosenthal

### AN ALGEBRAIC APPROACH FOR DECODING SPREAD CODES

E. Gorla, F. Manganiello and J. Rosenthal Journal Paper

In this paper we study spread codes: a family of constant-dimension codes for random linear network coding. In other words, the codewords are full-rank matrices of size $k\times n$ with entries in a finite field $\mathbb{F}_{q}$. Spread codes are a family of optimal codes with maximal minimum distance. We give a minimum-distance decoding algorithm which requires $\mathcal{O}((n-k)k^3)$ operations over an extension field $\mathbb{F}_{q^k}$. Our algorithm is more efficient than the previous ones in the literature, when the dimension $k$ of the codewords is small with respect to $n$. The decoding algorithm takes advantage of the algebraic structure of the code, and it uses original results on minors of a matrix and on the factorization of polynomials over finite fields.

17 JAN 2012

PhD Theses

### SPREAD CODES AND MORE GENERAL NETWORK CODES

F. Manganiello Theses

31 JUL 2011

### ON CONJUGACY CLASSES OF SUBGROUPS OF THE GENERAL LINEAR GROUP AND CYCLIC ORBIT CODES

#### In the proceeding of the 2011 IEEE International Symposium on Information Theory (ISIT)

Find it is the proceedings of the workshop.

Conference Proceedings with A.L. Trautmann-Horlemann and J. Rosenthal

### ON CONJUGACY CLASSES OF SUBGROUPS OF THE GENERAL LINEAR GROUP AND CYCLIC ORBIT CODES

F. Manganiello, A.L. Trautmann-Horlemann and J. Rosenthal Conference Proceedings

Orbit codes are a family of codes applicable for communications on a random linear network coding channel. The paper focuses on the classification of these codes. We start by classifying the conjugacy classes of cyclic subgroups of the general linear group. As a result, we are able to focus the study of cyclic orbit codes to a restricted family of them.

30 AUG 2010

### ORBIT CODES — A NEW CONCEPT IN THE AREA OF NETWORK CODING

#### In the proceeding of the 2010 IEEE Information Theory Workshop (ITW)

Find it is the proceedings of the workshop.

Conference Proceedings with A.L. Trautmann-Horlemann and J. Rosenthal

### ORBIT CODES — A NEW CONCEPT IN THE AREA OF NETWORK CODING

A.L. Trautmann-Horlemann, F. Manganiello and J. Rosenthal Conference Proceedings

We introduce a new class of constant dimension codes called orbit codes. The basic properties of these codes are derived. It will be shown that many of the known families of constant dimension codes in the literature are actually orbit codes.

6 JUL 2008

#### In the proceeding of the 2008 IEEE International Symposium on Information Theory (ISIT)

Find it is the proceedings of the workshop.

Conference Proceedings with E. Gorla and J. Rosenthal

### ON CONJUGACY CLASSES OF SUBGROUPS OF THE GENERAL LINEAR GROUP AND CYCLIC ORBIT CODES

F. Manganiello, E. Gorla and J. Rosenthal Conference Proceedings

In this paper we introduce the class of spread codes for the use in random network coding. Spread codes are based on the construction of spreads in finite projective geometry. The major contribution of the paper is an efficient decoding algorithm of spread codes up to half the minimum distance.

9 MAY 2008

### COMPUTATION OF THE WEIGHT DISTRIBUTION OF CRC CODES

#### Applicable Algebra in Engineering, Communication and Computing, 19(4):349-363

Find it in the journal.

Journal Paper

### COMPUTATION OF THE WEIGHT DISTRIBUTION OF CRC CODES

F. Manganiello Journal Paper

In this article, we illustrate an algorithm for the computation of the weight distribution of CRC codes. The recursive structure of CRC codes will give us an iterative way to compute the weight distribution of their dual codes starting from some “representative” words. Thanks to MacWilliams’ Theorem, the computation of the weight distribution of the dual codes can be easily brought back to that of CRC codes.

27 OCT 2005

Master Theses

### CALCOLO DELLA DISTRIBUZIONE DEI PESI NEI CODICI CICLICI ACCORCIATI

F. Manganiello Theses

.04

## AWARDS & GRANTS

• AWARDS
• 2019

• GRANTS
• 2019
2022

### NSF GRANT ECCS-1912702 - Co-PI

Awarded amount: $379,998 Other investigators: Y. Wang (PI) • 2016 2021 ### NSF GRANT DMS-1547399 - PI #### RTG: CODING THEORY, CRYPTOGRAPHY AND NUMBER THEORY Awarded amount:$2,126,971
Other investigators: S. Gao (Co-PI) and K. James (Co-PI)
Visit the homepage of the group for further information.
• 2012
2013

### Swiss NSF GRANT 138738 - PI

#### CODES, ALGORITHMS AND CRYPTOGRAPHY FOR RANDOM LINEAR NETWORK CODING

Fellowships for prospective researchers
• 2011
2012

### Swiss NSF GRANT 135934 - PI

#### CODES, ALGORITHMS AND CRYPTOGRAPHY FOR RANDOM LINEAR NETWORK CODING

Fellowships for prospective researchers
• CONFERENCE GRANTS
• 2017

### IEEE

#### SHANNON CENTENNIAL EVENT AT CLEMSON UNIVERSITY

Awarded amount: \$2,650
.05

## RESEARCH

LAB TEAM

### POSTDOCTORAL FELLOW

Dr. Machado joined the SMSS in August 2021 and his expertise are in coding theory and its applications to privacy and security.

### RTG POSTDOCTORAL FELLOW

Dr. Skelton joined the RTG group in August 2021. His expertises are in commutative algebra and combinatorics and will assist the RTG group in answering fundamental questions in coding theory and crypotography.

### RESEARCH ASSISTANT

His research interest was in number theory and is now expanding it to coding theory and cryptography.

### RESEARCH ASSISTANT

Her research interest is in post-quantum cryptography and is co-advised with Dr. Cartor.

FORMER TEAM MEMBERS

#### Postdoctoral fellows

• Ryann Cartor (Postoctoral Fellow - 2019-2021) now assistant professor at Clemson University.
• Hiram H. López (Postoctoral Fellow - 2016-2018) now assistant professor at Cleveland State University.
• Nina Rupert (RTG Postoctoral Fellow - 2017-2018) now course instructor at Western Governor University.

• Travis Baumbaugh (PhD Student - 2014-2020) now Cryptographer at ToposWare.

• Harrison Eggers (Master student - 2019-2020)
• Kristen Savary (Master student - 2017-2019)
• Alexander Joyce (Master student - 2017-2019)
.06

## TEACHING

• CURRENT
• Fall
2021

### MATH 1060 - Calculus in one variable I

#### Clemson University - Undergraduate Class

• TEACHING HISTORY at Clemson University

Fall 2020
• ### MATH 2190 - Introduction to mathematical Cryptography

#### Clemson University - Undergraduate Class

Spring 2019 and Spring 2017
• ### MATH 3110 - Linear Algebra

#### Clemson University - Undergraduate Class

Spring 2014, Fall 2014, Fall 2015, Fall 2016, Fall 2017, Fall 2018, Summer 1 2019, Summer 1 2019 and Summer 1 2021

Fall 2014

• ### MATH 8570 - Cryptography

#### Clemson University - Graduate Class

Spring 2015 and Spring 2021
• TEACHING HISTORY prior to Clemson University

Fall 2012

Spring 2011

Spring 2008
.07

## CONFERENCES

• VIRTUAL
• since APR 2021

### ACCESS - Algebraic Coding and Cryptography on the East coast Seminar Series - Seminar series - organizer

#### HOMEPAGE

with G. Matthews and E. Persichetti
• PLANNED
• APR 2022

### Algebraic Methods in Coding Theory and Communication - Workshop - organizer

#### Casa Matemática Oaxaca-BIRS, Oaxaca, Mexico

with E. Gorla, M. Greferath and H. López
• ORGANIZED
• OCT 2020

### Coding Theory, Cryptography, and Number Theory - AMS Special Sessions

#### AMS Fall Southeastern Virtual Sectional Meeting

with R. Cartor, S. Gao and K. James
• JAN 2020

### Coding Theory and Applications - AMS Special Session - organizer

#### AMS-MAA Joint Mathematics Meetings - Denver, CO, USA

with A. Beemer, I. Blake, C. Kelley
• JAN 2018

### Coding Theory and Applications - AMS Special Session

#### AMS-MAA Joint Mathematics Meetings - Baltimore, MD, USA

with H. López and G. Matthews
• AUG 2017

### Coding theory - Minisymposia

#### SIAM Conference on Applied Algebraic Geometry (AG17), Atlanta, GA, USA

with A. Ravagnani
• MAR 2017

### Coding Theory, Cryptography, and Number Theory - AMS Special Sessions

#### AMS Sectional Meetings - Charleston, SC, USA

with J. Brown, S. Gao, K. James and G. Matthews
• DEC 2016

### Shannon Centennial Event at Clemson

#### Clemson University - Clemson, SC, USA

with S. Gao, G. Matthews and Mike Pursley
• APR 2016

### Meeting on Algebraic Geometry for Applications (MAGA16)

#### Clemson University - Clemson, SC, USA

with M. Burr and S. Poznanovikj
• AUG 2015

### Coding theory - Minisymposia

#### SIAM Conference on Applied Algebraic Geometry (AG15) - Daejeon, South Korea

with A. Ravagnani
• JAN 2015

### Advances in Coding Theory - AMS Special Session

#### AMS-MAA Joint Mathematics Meetings - San Antonio, TX, USA

with G. Matthews and J. Walker


text:
PortOpt [Portfolio Optimizer] is an open-source (LGPLed) C++ program (with Python binding) implementing the Markowitz(1952) mean-variance model with agent's linear indifference curves toward risk in order to find the optimal assets portfolio under risk.

You have to provide PortOpt (in text files or - if you use the api- using your own code) the variance/covariance matrix of the assets, their average returns and the agent risk preference.

It returns the vector of assets' shares that compose the optimal portfolio.

In order to minimise the variance it internally uses QuadProg++, a library that implement the algorithm of Goldfarb and Idnani for the solution of a (convex) Quadratic Programming problem by means of an active-set dual method.

Windows executable (command line tool!), linux (x64) executable and source code (for C++/Python) are available from SourceForge.

Bugs and support

If you find a bug, request a feature or need support open a ticket or discuss it in the SourceForge pages.

Theorical Background

In portfolio theory agents attempts to maximise portfolio expected return for a given amount of portfolio risk, or equivalently to minimise risk for a given level of expected return.

The portfolio management can be portrayed graphically as in the above Figure, where the feasible set of variance-profitability combinations in enclosed by the blue curve and the B-D segment represents the efficient frontier, where no variance can be lowered at productivity's price or equivalently no productivity can be increased at price of increasing variance.

In order to simplify computations, forest managers are assumed to have risk aversion with simple linear preferences, that is they are willing to trade off variance with productivity proportionally. In such case the indifference curves can be drawn like a bundle of straight lines having equation $prod = \alpha * var + \beta$, where $\alpha$ is the linear risk aversion coefficient and both $prod$ and $var$ refer to the overall portfolio's productivity and variance.

Point $B$ represents the point having the lowest possible portfolio variance. Agents with $\alpha$ risk aversion will choose however the tangent point $C$ that can be obtained by solving the following quadratic problem:

$$\begin{array}{rrrll} \max_{x_i, \beta} & Y & = & \beta & \\ s.t. & & & & \\ & x_i & \geqslant & 0 & \forall i\\ & \sum_i x_i & = & 1 & \\ & \sum_i {x_i p_i} & = & \alpha \sum_i { \sum_j { x_i x_j \sigma_{i,j}}} + \beta & \\ \end{array} \label{eq:optimisation_problem1}$$

that by substitution become:

$$\begin{array}{rrrll} \min_{x_i} & Y & = & \alpha \sum_i { \sum_j { x_i x_j \sigma_{i,j}}} - \sum_i {x_i p_i} & \\ s.t. & & & & \\ & x_i & \geqslant & 0 & \forall i\\ & \sum_i x_i & = & 1 & \\ \end{array} \label{eq:optimisation_problem2}$$

where $x_i$ is the share of the asset $i$, $p_i$ is its productivity, $\sigma_{i,j}$ is the covariance between assets $i$ and $j$ and hence $\sum_i {x_i p_i}$ is the overall portfolio productivity and $\sum_i { \sum_j { x_i x_j \sigma_{i,j}}}$ is its variance.

As the only quadratic term arises when $i=j$ and $\sigma_{i,j}$ being the variance is always positive, the problem is convex and hence easily numerically solved.

Compilation (not needed if using a pre-compiled version)

Option 1 - as a stand-alone program

g++ -std=c++0x -O -o portopt_executable QuadProg++.cpp Array.cpp anyoption.cpp portopt.cpp  main.cpp

Option 2 - as a library to be used in your C/C++ program

g++ -fPIC -std=c++0x -O -c QuadProg++.cpp Array.cpp anyoption.cpp portopt.cpp main.cpp
g++ -std=c++0x -O -shared -Wl,-soname,portopt.so -o portopt.so QuadProg++.o Array.o anyoption.o portopt.o

g++ -std=c++0x -O -o portopt_executable main.o -Wl,-rpath,'\$ORIGIN' -L . portopt.so
./portopt_executable

Option 3 - as a lib to be used in python, using swig

swig -c++ -python portopt.i
g++ -fPIC -std=c++0x -O -c QuadProg++.cpp Array.cpp anyoption.cpp portopt.cpp portopt_wrap.cxx main.cpp -I/usr/include/python2.7 -I/usr/lib/python2.7
g++ -std=c++0x -O -shared -Wl,-soname,_portopt.so -o _portopt.so QuadProg++.o Array.o anyoption.o portopt.o portopt_wrap.o

(then please refer to the python example for usage)

If you want to change the output library name (e.g. you want to create _portopt_p3.so for python3 alongside _portopt.so for python2), do it in the %module variable of portopt.i and in the -soname and -o options of the linking command (and don't forget to use the right python included directory in the compilation command).
You can then load the correct module in your script with something like:

import sys
if sys.version_info < (3, 0):
import portopt
else:
import portopt_p3 as portopt

Usage

Please notice that the API changed from version 1.1, with the introduction of the port_opt_mean and port_opt_var parameters (both by reference). For the old 1.1 call instructions see here.

Linux
./portopt [options]
Windows
portopt.exe [options]

(from a DOS prompt: (a) START→run→“cmd”; (b) cd \path\to\portopt )

As a lib from C++:

Call:

double solveport (const vector< vector <double> > &VAR, const vector<double> &MEANS, const double &alpha, vector<double> &x_h, int &errorcode, string &errormessage, double &port_opt_mean, double &port_opt_var, const double tollerance = 0.000001)
As a lib using Python:
import portopt
results = portopt.solveport(var,means,alpha,tolerance) # tolerance is optional, default to 0.000001
functioncost = results[0]
shares       = results[1]
errorcode    = results[2]
errormessage = results[3]
opt_mean     = results[4]
opt_var      = results[5]

Options

  -h  --help                                   Prints this help
-v  --var-file [input_var_file_name]         Input file containing the variance/covariance matrix (relative path)
-m  --means-file [input_means_file_name]     Input file containing the means vector (relative path)
-a  --alpha [alpha_coefficient]              Coefficient between production and risk in the linear indifference curves
-f  --field-delimiter [field_delimiter]      Character to use as field delimiter (default: ';')
-s  --decimal-separator [decimal-separator]  Character to use as decimal delimiter (default: '.')
-t  --tollerance [tolerance]                 A tolerance level to distinguish from zero (default: 0.000001)

Notes

• Higher the alpha, lower the agent risk aversion;
• Set a negative alpha to retrieve the portfolio with the lowest possible variance;
• Set alpha to zero to retrieve the portfolio with the highest mean, independently from variance (solution not guaranteed to be unique);
• Assets shares are returned in the x_h vector, eventual error code (0: all fine, 1: input data error, 2: no solutions, 3: didn't solve, 4: solver internal error) in the errorcode parameter.
• Use option “tollerance” with two l up to version 1.1 included

PortOpt is free software: you can redistribute it and/or modify it under the terms of the GNU Lesser General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.

PortOpt is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

You should have received a copy of the GNU Lesser General Public License along with PortOpt. If not, see http://www.gnu.org/licenses.

Citations

If you use this program or a derivative of it in an academic framework, please cite it!

format: plain


text:
# Does the capacitance depend on the distance?

I know that the Capacitance of a capacitor does not depend on the Voltage (because it is a measure for how much charge a capacitor can hold) and it largely depends on the Area

i.e. it holds that : $$C= \frac{Q}{U}$$ but it also holds that : $$C= \epsilon \frac{A}{d}$$ where Q is charge, U is voltage, A is area, d is the distance , epsilon is the electric field constant

Is it true that the capacitance depends only on: area, and distance from the plate of eachother ?

For a parallel plate capacitor yes, the capacitance only depends on the plate area and plate separation.

This is a good example of knowing what your equations mean, and you are on the right track. The definition of capacitance we use $$C=Q/U$$ is true for a given capacitor with capacitance $$C$$, but it just gives a proportionality between the charge on the plates and the potential difference between them. If we wanted to rearrange the equation to show more of the "cause and effect" we would say $$Q=CU$$, meaning if we increase the potential difference between the plates, we know what charges will end up on the plates. However, I wouldn't say the capacitance "depends" on these things, since changing either $$Q$$ or $$U$$ does not actually change the capacitance, since if we change one the other changes in proportion according to $$C$$.

On the other hand, the equation $$C=\epsilon A/d$$ does show us actual dependencies. We can change the area and actually change the capacitance (How $$Q$$ and $$U$$ relate), or we change change the plate separation to actually change the capacitance. Changing one doesn't automatically change the other. In terms of the geometry, these are the only two things that matter. (We could include a dielectric between the plates, then there is more things that effect capacitance than just the geometry of the system).

Notice that by just having the equations there is no way for us to know any of this. Only when we know what the equations mean and what capacitance actually is physically can we make this sort of analysis of the equations in terms of what they tell us about the physical world.

• There's also an implicit assumption that the parallel plates are very close together. If they're not, then the size and shape of the plates does matter as well. – Michael Seifert Dec 19 '18 at 15:44
• @MichaelSeifert Yes that equation does assume "infinitely large and infinitesimally thin" plates. – Aaron Stevens Dec 19 '18 at 15:56

As you infer, the capacitance of an object determines that ratio of charge separation to the voltage associated with that separation: $$\frac{Q}{U}=C$$ using the same symbols as in the question. If $$Q=0$$, then $$U=0$$, but $$C$$ is non-zero.

The ability of a device to hold charge depends on the mechanical structure and geometry of the device, and the resulting potential difference between the locations of separated charges is proportional to the charge.

For two parallel plates, the ratio, geometrically, works out to $$C= \epsilon\frac{A}{d}.$$ Two conducting parallel plates, charged or not, have this capacitance. On the other hand, the capacitance of two concentric spherical shells is related not to an area, but to the product of the radii of the shells, $$a$$ and $$b$$, $$a < b$$: $$C=4\pi\epsilon\frac{a b}{b-a}$$ If we expand the outer shell to infinity, and leave the inner shell at radius $$a$$, we get that a single spherical shell has a capacitance of $$C=4\pi\epsilon a.$$

So, the answer to your question is "maybe". For the concentric spherical shell, it doesn't depend on the area in the formula, but on the product of the radii, which has area units. But one might conceptually think of $$4\pi a$$ as the area divided by the radius.

But the geometric formula you give for the capacitance is only directly applicable to parallel-plate capacitors.


text:
# Summation of Reciprocal of Zero of Order 1 Bessel Function by Order 0 Bessel Function of it

## Theorem

$\displaystyle \sum_{n \mathop = 1}^\infty \dfrac 1 {x_n \map {J_0 } {x_n} } = 0 \cdotp 38479 \ldots$

where:

$x_n$ is the $n$th zero of the order $1$ Bessel function of the first kind
$\map {J_0 } {x_n}$ is the order $0$ Bessel function of the first kind of $x_n$.

## Historical Note

This result is reported in François Le Lionnais and Jean Brette: Les Nombres Remarquables of $1983$, with no indication of context.

It is not revealed why this result is significant.


text:
USRP Hardware Driver and USRP Manual  Version: 4.3.0.0-77-gc27519624 UHD and USRP Manual
Building and Installing UHD from source

# Build Dependencies

Linux Notes: This is dependent on the distribution you are using, but most, if not all, of the dependencies should be available in the package repositories for your package manager.

Mac OS X Notes: Install the Xcode app to get the build tools (GCC and Make). Use MacPorts to get the Boost and Mako dependencies. Other dependencies can be downloaded as DMG installers from the web or installed via MacPorts. See the UHD OS X build instructions for more information: Build Instructions (Mac OS X)

Windows Notes: The dependencies can be acquired through installable EXE files. Usually, the Windows installer can be found on the project's website. Some projects do not host Windows installers, and if this is the case, follow the auxiliary download URL for the Windows installer (below).

### C++ Compiler

The following compilers are known to work and officially supported:

• GCC >= 6.3.0
• Clang >= 6.0.0
• MSVC >= 15.0; the free version works. Users need to install the "Desktop Development with C++" Workload for Visual Studio. On Windows, it can be found in: Tools -> Get Tools and Features... -> Workloads -> Windows

Other compilers (or lower versions) may work, but are unsupported.

### CMake

For Windows users, copy the CMake file to Program Files, e.g. C:\Program Files\cmake-3.13.4-win32-x86. The CMake path, e.g. C:\Program Files\cmake-3.13.4-win32-x86\bin needs to be added to the environment variables.

### Boost

The Boost binary installer must be selected to match the architecture of Windows being run.

### LibUSB

The directory to which you extract libusb must not contain spaces. This is to say that C:\local\lib usb-1.0.22 will cause compile issues moving forward.

### Python

• Purpose: Used by mako build time, and utility scripts and the Python API at runtime
• Minimum Version: 3.5
• Usage: build time + runtime utility scripts (required)
• The Python binary installer must be selected to match the system processor. Although, the 32-bit Python version can be used with 32-bit or 64-bit Windows system, it is recommended to match between Python and Windows installers. If the system is occupied with 64-bit Windows and x64-based processor, the Windows x86-64 MSI Installer -> python-version.amd64.msi needs to be used.
• The Python path needs to be added to the environment variables.
• Install fundamental packages for Python: On Windows Terminal, navigate to Python scripts folder, e.g. C:\local\Python37\Scripts, and execute the following commands to install requests and numpy packages, respectively:

pip3 install requests pip3 install numpy pip3 install ruamel.yaml pip3 install setuptools

• For curses package installation:

• Download a package that is similar to the Python version, Windows System, and system processor and copy it to Python scripts folder. For example, for Python 3.7, 64-bit Windows, and x64-based processor, download the curses-2.2-cp37-cp37m-win_amd64.whl.
• Install the package dependency, wheel package:

pip3 install wheel

• Install the curses package and include it to Python scripts:

python3 -m pip3 install curses-2.2-cp37-cp37m-win_amd64.whl

### Mako

• Purpose: source code generation
• Minimum Version: 0.4.2
• Usage: build time (required)
• Alternative method: You can use pip3 or easy_install to install Mako from PyPi. To install it using 'pip3' on Windows, navigate to Python scripts folder, e.g. C:\local\Python37\Scripts, and run the following command:

pip3 install mako

### NSIS

• Purpose: create Windows installers. It is used to create binary packages of UHD enabling easy distribution and installation of UHD, associated utilities, and examples.
• Recommended Version: 3.04
• Usage: build time (optional)

### Git

Required to check out the repository (not necessary if building from tarballs).

On Windows, install Cygwin from https://www.cygwin.com/ with Git support to checkout the repository or install msysGit from http://code.google.com/p/msysgit/downloads/list.

## Setting up the dependencies on Ubuntu

You can install all the dependencies through the package manager:

sudo apt-get install autoconf automake build-essential ccache cmake cpufrequtils doxygen ethtool \
g++ git inetutils-tools libboost-all-dev libncurses5 libncurses5-dev libusb-1.0-0 libusb-1.0-0-dev \
libusb-dev python3-dev python3-mako python3-numpy python3-requests python3-scipy python3-setuptools \
python3-ruamel.yaml

## Setting up the dependencies on Fedora

You can install all the dependencies through the package manager:

sudo yum -y install boost-devel libusb1-devel doxygen python3-docutils python3-mako python3-numpy python3-requests python3-ruamel-yaml python3-setuptools cmake make gcc gcc-c++

or

sudo dnf -y install boost-devel libusb1-devel doxygen python3-docutils python3-mako python3-numpy python3-requests python3-ruamel-yaml python3-setuptools cmake make gcc gcc-c++

# Getting the source code

git clone https://github.com/EttusResearch/uhd.git

Our source code repository contains of the following branches:

• master: This is the main development branch, with updated new features and bug fixes.
• UHD-*: These branches are created from master upon a release or release candidate. They are used to create releases within a stable release cycle, and usually only receive bugfixes. For example, all 3.14.* releases are taken from the same branch (UHD-3.14). These branches usually no longer receive updates once the following major release branch is created (for example, when the UHD-3.14 branch was created, the UHD-3.13 branch would only receive updates under special circumstances).
• UHD-*.LTS: These are long-term support branches. They serve the same purpose as the other UHD-* branches, but generally receive bugfixes for much longer.

We might also be publishing experimental feature branches which can then be found in the same repository. All of our versioned releases are associated with tags in the repository.

# Using PyBOMBS

PyBOMBS is a command-line tool for Linuxes (and some Unixes) from the GNU Radio ecosystem and will do a source build of UHD, including setting up prerequisites/dependencies (regardless of the distribution). Assuming you have PyBOMBS set up, you can install UHD with the following command:

$pybombs install uhd  Head to the PyBOMBS Homepage for more instructions. PyBOMBS can install UHD (as well as GNU Radio or similar projects) both into system directories as well as into user's home directories, omitting the requirement for superuser access. # Build Instructions (Unix) ## Generate Makefiles with CMake cd <uhd-repo-path>/host mkdir build cd build cmake ../  Additionally, configuration variables can be passed into CMake via the command line. The following common-use configuration variables are listed below: • For a custom install prefix: -DCMAKE_INSTALL_PREFIX=<install-path> • To install libs into lib64: cmake -DLIB_SUFFIX=64 Example usage: cmake -DCMAKE_INSTALL_PREFIX=/opt/uhd ../  Ubuntu 20.04 note: When building for Ubuntu 20.04, you may run into errors such as this during CMake's generation stage: CMake Error in python/CMakeLists.txt: Imported target "Boost::chrono" includes non-existent path "/include" in its INTERFACE_INCLUDE_DIRECTORIES. Possible reasons include: The path was deleted, renamed, or moved to another location. An install or uninstall procedure did not complete successfully. The installation package was faulty and references files it does not provide.  These errors occur when CMake finds filesystem items by following the /bin symlink to /usr/bin and thus incorrectly calculating the root path for various directories needed by the build. If you encounter this issue, ensure that /usr/bin appears before /bin in the PATH environment variable of the process executing CMake. Alternatively, you can pass the CMAKE_FIND_ROOT_PATH configuration variable to CMake with a value of /usr to point it to the right starting directory for filesystem item searches. Example usage: cmake -DCMAKE_FIND_ROOT_PATH=/usr ../  ## Build and install make make test # This step is optional sudo make install  ## Setup the library path (Linux) Make sure that libuhd.so is in your LD_LIBRARY_PATH, or add it to /etc/ld.so.conf and make sure to run: sudo ldconfig  ## Compiling for ARM platforms When compiling for ARM platforms, the assumption is made that NEON extensions are available if the arm_neon.h header is found. However, this might not be true, e.g., when cross-compiling for an arm7l target (e.g., the Odroid XU4) using a standard SDK. In this case, it's necessary to tell CMake to disable NEON extensions: cmake -DNEON_SIMD_ENABLE=OFF [...]  # Build Instructions (Windows) ## Generate the project with CMake • Make sure the version of Python that CMake detects matches the version you want it to be (check the PYTHON_VERSION variable) • Open the CMake GUI. • Set the path to the source code: <uhd-repo-path>/host. • Set the path to the build directory (this may require creating the folder \build\): <uhd-repo-path>\host\build. • Make sure that the paths do not contain spaces. • Check the Advanced checkbox. • Click "Configure". • Set "Microsoft Visual Studio 10" as the compiler. Select the recent MSVC that is available on the machine. • Click “Finish” and allow CMake to Generate • Set or add the build variables with type PATH • Boost_INCLUDE_DIR should point to the PATH where the Boost .hpp files are, e.g. C:\local\boost_version\ • Boost_LIBRARY_DIR should point to the pre-built libraries, e.g. C:\local\boost_version\lib64-msvc-14.0) • If a release UHD build is required: • Click on "Generate", and a project file will be created in the build directory. • If a debug UHD build is required: • Click on Grouped • Click on CMAKE • Look for the parameter CMAKE_BUILD_TYPE: Release and change it to CMAKE_BUILD_TYPE: Debug. • Click on "Generate", and a project file will be created in the build directory. ## Compile and Install with Visual Studio • Open the <uhd-repo-path>\host\build\ALL_BUILD.vcxproj in visual studio, generate the project. Watch the output console for errors. • If you did not specify a CMAKE_INSTALL_PREFIX where your user has write privileges, you must close Visual Studio, run it again with Administrator Privileges, and open ALL_BUILD.vcxproj. • Right click on the INSTALL project in the project explorer, generate it. Watch the output console for errors. ## LibUSB notes On Windows, CMake does not have the advantage of pkg-config, so we must manually tell CMake how to locate the LibUSB header and lib. • From the CMake GUI, select "Advanced View". • Set or add the following entry with type PATH LIBUSB_INCLUDE_DIRS to the directory for libusb.h, e.g. C:\local\libusb-1.0.22\include\libusb-1.0. • Set or add the following entry with type FILEPATH LIBUSB_LIBRARIES to the full path for libusb-1.0.lib, e.g. C:\local\libusb-1.0.22\MS64\dll\libusb-1.0.lib. • Recommend the static libusb-1.0.lib to simplify runtime dependencies. • Check the box to enable USB support, click "Configure" and "Generate". Note: On Windows, LibUSB v1.0.19 is required to use most USB3 controllers. ## Build the project in MSVC • Open the generated project file in MSVC, e.g. C:\cygwin64\home\admin\uhd\host\build\UHD.sln. • Change the build type from "Debug" to "Release". • Select the "Build All" target, right-click, and choose "Build". • Select the install target, right-click, and choose "Build". Note: You may not have permission to build the install target. You need to be an administrator or to run MSVC as administrator. ## Build the project in MSVC (command line) Open the Visual Studio Command Prompt Shorcut: cd <uhd-repo-path>\host\build DevEnv uhd.sln /build Release /project ALL_BUILD DevEnv uhd.sln /build Release /project INSTALL  ## Compiling a binary installer • Building the "PACKAGE" project will produce a binary installer if NSIS is installed. This installer will be for either 64 bit or 32 bit as chosen during the CMake step. • Select the "PACKAGE" project in the Solution Explorer, right-click, and choose "Build". ## Setup the PATH environment variable Add the UHD bin path to PATH% (usually C:\Program Files\UHD\bin) Note: The default interface for editing environment variable paths in Windows is very poor. We recommend using "Rapid Environment Editor" (http://www.rapidee.com) over the default editor. # Build Instructions (Mac OS X) ### X11/XQuartz or Terminal For the purposes of building and using UHD, you can use Apple's Terminal.app if you so choose, no matter how you install UHD. That said, running almost any graphical interface (GUI) will require downloading and installing X11/XQuartz first. Through OSX 10.8, Apple provided a means to install X11.app, but XQuartz has always been more up to date. Staring in 10.9, Apple no longer provides a full working version of X11.app. Hence, just use XQuartz from the get-go. Note that unless you experiment with using the Quartz interface to various graphical toolkits (e.g., GTK), you must use X11 as the terminal interface for any GUI applications. ### Xcode Apple provides a fully integrated development environment via their Xcode toolkit, which can be downloaded either via the App store or directly from Apple's Developer area depending on the version of OSX in use. Xcode provides the compilers and related development tools needed to build or execute UHD and its dependencies. Once Xcode is installed, you must still install the Command Line Tools, which can be accomplished by running Xcode.app, then going to Preferences... -> Downloads and making sure Command Line Tools is selected/enabled [feel free to select other downloads too]. You might be able to install the Command Line Tools in a terminal using xcode-select --install  but this command will not work with every OSX / Xcode combination (e.g., does not work with OSX 10.8 and Xcode 5, but does work with OSX 10.9 and Xcode 5). Once the Command Line Tools are installed, UHD and other projects can be installed either from source or, preferably, via MacPorts. ### Background Dependencies There are a number of background libraries and applications that must be installed from source or binary in order to compile or execute UHD; for a full list, see Build Dependencies. These can be obtained by using MacPorts, Fink, HomeBrew, and/or from source / scratch. MacPorts tends to be more up-to-date with respect to new releases, which can be both a blessing and a curse since sometimes new released are untested and result in build or runtime errors. MacPorts, HomeBrew, and Fink offer thousands of ready-to-install libraries and applications, and hence they are highly recommended to use instead of installing from source / scratch. Many UHD developers first install UHD using MacPorts in order to get all of the necessary background dependencies installed, then remove just UHD via sudo port install uhd sudo port uninstall uhd  NOTE: We highly recommended that all dependencies be installed via the same package manager! When issues arise, they are much easier to track down, and updating to newer versions of UHD as well as dependencies is much easier. NOTE: Other package managers (e.g., Fink, HomeBrew) will require different commands than the above to install all dependencies and then remove the UHD install. Please consult the specific package manager in use for how to do these commands properly; they will not be covered here. #### Compiling UHD from Source Installing UHD from source follows the standard cmake method as found in many places, with a few arguments to make sure cmake always finds the correct version of Python, and uses the desired compiler. First, download the source code either via a release or via GIT. For example, on OSX 10.8+ and using Xcode's legacy Apple GCC (via llvm), MacPorts installed into /opt/local (the default), and for Python 2.7 as installed by MacPorts, issue the following commands from within the UHD source directory: $ mkdir build
$cd build$ CC=/usr/bin/llvm-gcc CXX=/usr/bin/llvm-g++ cmake -DCMAKE_INSTALL_PREFIX=/opt/local -DPYTHON_EXECUTABLE=/opt/local/bin/python2.7 -DPYTHON_INCLUDE_DIR=/opt/local/Library/Frameworks/Python.framework/Versions/2.7/Headers -DPYTHON_LIBRARY=/opt/local/Library/Frameworks/Python.framework/Versions/2.7/Python ../host
$make  If make succeeds, then you can test the build for errors via $ make test

To install the build, issue

\$ sudo make install

Selecting another compiler is as simple as changing the CC and CXX pre-arguments to the cmake command. Similarly, one can change the install prefix by changing the setting of the variable CMAKE_INSTALL_PREFIX.

NOTE: All of the PYTHON defines must point to the same install of Python, otherwise runtime errors are likely to occur.

NOTE: When using some other package manager (e.g., Fink, HomeBrew), the actual variable settings (-D...=...) will be different than those above. Please consult the specific package manager in use for how to do these settings properly; they will not be covered here.

• After installing, you might want to download the FPGA images packages by running uhd_images_downloader on the command line, or one of these executables (the actual path may differ based on your installation):
• Mac OS X: In MacPorts, when UHD is installed the images are automatically downloaded and installed into their proper location. For any other package manager or install method, you should execute the uhd_images_downloader.py script to get the images installed appropriately.
• For USB-Based devices, make sure to read USB Transport (LibUSB) for platform-specific post-installation tasks.

# Building applications that require UHD using CMake

If your application uses CMake as a build system, the following command will setup up your build environment to link against UHD:

find_package(UHD "3.10.0")

This will set the CMake variable UHD_INCLUDE_DIRS and UHD_LIBRARIES accordingly.

See the example in examples/init_usrp for more details, as well as the UHDConfig.cmake file that gets installed along with the UHD libraries.

# Static Builds

Using CMake, UHD can be built as a static library by switching on ENABLE_STATIC_LIBS.

cmake -DENABLE_STATIC_LIBS=ON <path to UHD source>

When linking the static library, you must ensure that the library is loaded in its entirety, otherwise global objects aren't initialized at load-time and it will always fail to detect any devices. Also, all UHD dependencies for UHD must be provided unless your linker has other ways of resolving library dependencies.

With the GNU ld linker (e.g. on Linux platforms), this is done using the --whole-archive switch. Using the GNU C++ compiler, the correct command line is:

g++ your_uhd_app.cpp -Wl,-whole-archive <path to UHD libs>/libuhd.a -Wl,-no-whole-archive -ldl -lpthread -l<all other libraries>

Note that --whole-archive is disabled after including libuhd.a. The exact list of libraries depends on your UHD build. When using UHDConfig.cmake (see Building applications that require UHD using CMake), the path to libuhd.a is saved into UHD_LIBRARIES, and UHD_STATIC_LIB_DEPS lists the required dependencies. See UHDConfig.cmake for details.


text:
# Math Help - Polynomial Division

1. ## Polynomial Division

I divided (-4x^3 + x^2 - 4)/(x - 1) and got a totally different answer on three attempts than the book.

Here is the right answer:

-4x^2 - 3x - 3 remainder -7

How can this be?

Can you show me step by step why the above answer is correct?

2. Hello,
Originally Posted by magentarita
I divided (-4x^3 + x^2 - 4)/(x - 1) and got a totally different answer on three attempts than the book.

Here is the right answer:

-4x^2 - 3x - 3 remainder -7

How can this be?

Can you show me step by step why the above answer is correct?
My method may not be like yours, but I can't manage to change it ~~

$-4x^3+x^2-4$ and x-1.

First, I see the first term of the polynomial -4x^3 and the first term of x-1 : x.
$-4x^3={\color{green}-4x^2}(x)$.

So I'll write :
$-4x^3+x^2-4={\color{green}-4x^2}(x-\underbrace{{\color{red}1}){\color{red}-4x^2}}_{\text{this is 0}} \quad +x^2-4=-4x^2(x-1)-3x^2-4$

And so on... :

$-4x^2(x-1)-3x^2-4=-4x^2(x-1)-3x(x-1)-3x-4=(x-1)(-4x^2-3x)-3x-4$

$(x-1)(-4x^2-3x)-3x-4=(x-1)(-4x^2-3x)-3(x-1)-3-4$ $=\boxed{(x-1)(-4x^2-3x-3)\textbf{-7}}$

If you want to know where your mistake(s) is/are, just show your work ^^

3. ## Perfect!

Originally Posted by Moo
Hello,

My method may not be like yours, but I can't manage to change it ~~

$-4x^3+x^2-4$ and x-1.

First, I see the first term of the polynomial -4x^3 and the first term of x-1 : x.
$-4x^3={\color{green}-4x^2}(x)$.

So I'll write :
$-4x^3+x^2-4={\color{green}-4x^2}(x-\underbrace{{\color{red}1}){\color{red}-4x^2}}_{\text{this is 0}} \quad +x^2-4=-4x^2(x-1)-3x^2-4$

And so on... :

$-4x^2(x-1)-3x^2-4=-4x^2(x-1)-3x(x-1)-3x-4=(x-1)(-4x^2-3x)-3x-4$

$(x-1)(-4x^2-3x)-3x-4=(x-1)(-4x^2-3x)-3(x-1)-3-4$ $=\boxed{(x-1)(-4x^2-3x-3)\textbf{-7}}$

If you want to know where your mistake(s) is/are, just show your work ^^
Perfectly done!


text:
Home > Error Analysis > Error Analysis Differentiation

# Error Analysis Differentiation

## Contents

The error estimate is obtained by taking the square root of the sum of the squares of the deviations.

Proof: The mean of n values of x is: Let the error Anmelden 30 2 Dieses Video gefällt dir nicht? JSTOR2629897. ^ a b Lecomte, Christophe (May 2013). "Exact statistics of systems with uncertainties: an analytical theory of rank-one stochastic dynamic systems". In such instances it is a waste of time to carry out that part of the error calculation. http://axishost.net/error-analysis/error-analysis-immunochemistry-error-analysis.php

Anmelden Transkript Statistik 13.682 Aufrufe 29 Dieses Video gefällt dir? They yield results distributed about some mean value. In these terms, the quantity, , (3) is the maximum error. doi:10.1016/j.jsv.2012.12.009. ^ Lecomte, Christophe (May 2013). "Exact statistics of systems with uncertainties: an analytical theory of rank-one stochastic dynamic systems".

## Real Analysis Differentiation

Your cache administrator is webmaster. There may be extraneous disturbances which cannot be taken into account. Wird verarbeitet... Such accepted values are not "right" answers.

Example 1: If R = X1/2, how does dR relate to dX? 1 -1/2 dX dR = — X dX, which is dR = —— 2 √X

divide by the The best estimate of the true standard deviation is, . (7) The reason why we divide by N to get the best estimate of the mean and only by N-1 for The coeficients in each term may have + or - signs, and so may the errors themselves. Error Propagation Formula Physics Mean Value Suppose an experiment were repeated many, say N, times to get, , N measurements of the same quantity, x.

In a probabilistic approach, the function f must usually be linearized by approximation to a first-order Taylor series expansion, though in some cases, exact formulas can be derived that do not Wird geladen... For instance, no instrument can ever be calibrated perfectly. http://teacher.nsrl.rochester.edu/phy_labs/AppendixB/AppendixB.html Melde dich an, um unangemessene Inhalte zu melden.

But small systematic errors will always be present. Percent Error Calculus Wird geladen... Notice the character of the standard form error equation. Random counting processes like this example obey a Poisson distribution for which .

## Real Analysis Differentiation Problems

Thus 549 has three significant figures and 1.892 has four significant figures.

Conversely, it is usually a waste of time to try to improve measurements of quantities whose errors are already negligible compared to others. 6.7 AVERAGES We said that the process of Real Analysis Differentiation Random errors are errors which fluctuate from one measurement to the next. Partial Derivative Error Analysis Zeros to the left of the first non zero digit are not significant.

Certainly saying that a person's height is 5'8.250"+/-0.002" is ridiculous (a single jump will compress your spine more than this) but saying that a person's height is 5' 8"+/- 6" implies useful reference When is this error largest? Therefore, the propagation of error follows the linear case, above, but replacing the linear coefficients, Aik and Ajk by the partial derivatives, ∂ f k ∂ x i {\displaystyle {\frac {\partial The derivative of f(x) with respect to x is d f d x = 1 1 + x 2 . {\displaystyle {\frac {df}{dx}}={\frac {1}{1+x^{2}}}.} Therefore, our propagated uncertainty is σ f Error Analysis Division

Behavior like this, where the error, , (1) is called a Poisson statistical process. This modification gives an error equation appropriate for standard deviations. Random errors are unavoidable and must be lived with. my review here If one made one more measurement of x then (this is also a property of a Gaussian distribution) it would have some 68% probability of lying within .

Melde dich an, um dieses Video zur Playlist "Später ansehen" hinzuzufügen. Using Differentials To Estimate Error After addition or subtraction, the result is significant only to the place determined by the largest last significant place in the original numbers. If one were to make another series of nine measurements of x there would be a 68% probability the new mean would lie within the range 100 +/- 5.


text:
# Another Identities Crisis

Show 40 post(s) from this thread on one page
Page 2 of 2 First 12
• January 14th 2007, 12:22 PM
CaptainBlack
Quote:

Originally Posted by Freaky-Person
They're not. We have some identites but not these ones. All we have is 8 of the easiest ones. Anything multiplied or divided by two, or even associated with the angles is in the AP or Pre-calculus course. This is Canada for you...

Some of these are relatively trivial results of the sum and difference identities:

$\cos(A+B)=\cos(A)\cos(B)-\sin(A)\sin(B)$

Put $A=B$:

$\cos(2A)=\cos^2(A)-\sin^2(A)$

then using Pythagoras's theorem in the form:

$\cos^2(x)+\sin^2(x)=1$

we get:

$\cos(2A)=2\cos^2(A)-1$

and

$\cos(2A)=1-2\sin^2(A)$

and by putting $a=2A$

$\cos(a)=2\cos^2(a/2)-1$

and

$\cos(a)=1-2\sin^2(a/2)$

RonL
Show 40 post(s) from this thread on one page
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text:
## What are prime gaps and who is Yitang Zhang?

You have probably read a news about one professor proving The Prime Gap conjecture. In this post, I will give you an overview of what the excitement is all about in the mathematics community.

Prof. Yitan Zhang (courtesy of UNH via Slate.com)

This post is written for the high school students and those who are interested in mathematics that are non mathematics majors.

What are Prime Numbers?

Most of us are familiar with prime numbers. A prime number is a positive integer that is divisible only by 1 and itself.  The number 5 is a prime number, while 8 is not prime because 8 is divisible by 2 and 4. If we examine the 10 positive integers, it is easy to see that only four are prime numbers: 2, 3, 5 and 7. In the figure below, shown are the prime numbers less than 100. » Read more

## 4 Types of Composite Numbers You Probably Have Not Heard Of

There are numbers that are named because of their special characteristics. Prime numbers for example are unique because they only have two factors, 1 and itself.  Composite numbers, on the other hand, have more than two factors.

Speaking of composite numbers, there are different types of such numbers that you probably have not heard of. In this post, we familiarize ourselves with these types of numbers. » Read more

## Mersenne Primes Under the Microscope

What are Mersenne Primes?

The recent discovery of the largest known prime number which is 17 million digits highlighted the importance of Mersenne primes.  This newest prime number and the thirteen largest primes are all Mersenne primes. But what are Mersenne primes really and why are they important in finding the largest prime numbers?

If a prime number can be expressed in the form $2^n - 1$, $n$ an integer, then it is said to be a Mersenne prime. The name came from Marin Mersenne who studied them, a French monk and well-known mathematician in the 17th century.

Many early mathematicians saw and conjectured that if n is a prime number, $2^n - 1$ is prime.  For instance, in the figure above, for $n = 2, 3, 5, 7$ which are prime numbers, their corresponding $2^n - 1$ values are also prime numbers. However, this is not true in general since $2^{11} - 1 = 2047 = (23)(89)$ is not prime.  » Read more

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