text: References of "Charlier, Emilie"      in Complete repository Arts & humanities   Archaeology   Art & art history   Classical & oriental studies   History   Languages & linguistics   Literature   Performing arts   Philosophy & ethics   Religion & theology   Multidisciplinary, general & others Business & economic sciences   Accounting & auditing   Production, distribution & supply chain management   Finance   General management & organizational theory   Human resources management   Management information systems   Marketing   Strategy & innovation   Quantitative methods in economics & management   General economics & history of economic thought   International economics   Macroeconomics & monetary economics   Microeconomics   Economic systems & public economics   Social economics   Special economic topics (health, labor, transportation…)   Multidisciplinary, general & others Engineering, computing & technology   Aerospace & aeronautics engineering   Architecture   Chemical engineering   Civil engineering   Computer science   Electrical & electronics engineering   Energy   Geological, petroleum & mining engineering   Materials science & engineering   Mechanical engineering   Multidisciplinary, general & others Human health sciences   Alternative medicine   Anesthesia & intensive care   Cardiovascular & respiratory systems   Dentistry & oral medicine   Dermatology   Endocrinology, metabolism & nutrition   Forensic medicine   Gastroenterology & hepatology   General & internal medicine   Geriatrics   Hematology   Immunology & infectious disease   Laboratory medicine & medical technology   Neurology   Oncology   Ophthalmology   Orthopedics, rehabilitation & sports medicine   Otolaryngology   Pediatrics   Pharmacy, pharmacology & toxicology   Psychiatry   Public health, health care sciences & services   Radiology, nuclear medicine & imaging   Reproductive medicine (gynecology, andrology, obstetrics)   Rheumatology   Surgery   Urology & nephrology   Multidisciplinary, general & others Law, criminology & political science   Civil law   Criminal law & procedure   Criminology   Economic & commercial law   European & international law   Judicial law   Metalaw, Roman law, history of law & comparative law   Political science, public administration & international relations   Public law   Social law   Tax law   Multidisciplinary, general & others Life sciences   Agriculture & agronomy   Anatomy (cytology, histology, embryology...) & physiology   Animal production & animal husbandry   Aquatic sciences & oceanology   Biochemistry, biophysics & molecular biology   Biotechnology   Entomology & pest control   Environmental sciences & ecology   Food science   Genetics & genetic processes   Microbiology   Phytobiology (plant sciences, forestry, mycology...)   Veterinary medicine & animal health   Zoology   Multidisciplinary, general & others Physical, chemical, mathematical & earth Sciences   Chemistry   Earth sciences & physical geography   Mathematics   Physics   Space science, astronomy & astrophysics   Multidisciplinary, general & others Social & behavioral sciences, psychology   Animal psychology, ethology & psychobiology   Anthropology   Communication & mass media   Education & instruction   Human geography & demography   Library & information sciences   Neurosciences & behavior   Regional & inter-regional studies   Social work & social policy   Sociology & social sciences   Social, industrial & organizational psychology   Theoretical & cognitive psychology   Treatment & clinical psychology   Multidisciplinary, general & others     Showing results 41 to 60 of 66     1 2 3 4     S-automatic setsCharlier, Emilie Scientific conference (2010, December)In this talk, I will discuss some new properties of S-automatic sets. First I will show that a multidimensional set is S-automatic for all abstract numeration systems S if and only if it is 1-automatic ... [more ▼]In this talk, I will discuss some new properties of S-automatic sets. First I will show that a multidimensional set is S-automatic for all abstract numeration systems S if and only if it is 1-automatic. This result is surprising in the following sense: the class of multidimensional 1-automatic sets is a strict subclass of that of semi-linear sets. Hence, this result is not a generalization of the well-known result in integer base numeration systems: a multidimensional set is b-automatic for all integer bases b ≥ 1 if and only if it is semi-linear. Second I will describe the possible behaviors of the nth -term of an S-automatic set, depending on the growth function (i.e., the number of words of length n) of the numeration language. [less ▲]Detailed reference viewed: 31 (1 ULiège) Criteria for recognizability in abstract numeration systemsCharlier, Emilie Scientific conference (2010, October)In this talk, I will first shortly introduce abstract numeration systems. Then I will prove some first results I have regarding the growth function of recognizable sets. I will conjecture which functions ... [more ▼]In this talk, I will first shortly introduce abstract numeration systems. Then I will prove some first results I have regarding the growth function of recognizable sets. I will conjecture which functions can be the growth functions of recognizable sets in general, depending on the growth functions of the numeration language and of the sublanguage under consideration. [less ▲]Detailed reference viewed: 14 (0 ULiège) State complexity of testing divisibilityCharlier, Emilie ; Rampersad, Narad ; Rigo, Michel et alin McQuillan, Ian, Pighizzini, Giovanni (Ed.) Proceedings Twelfth Annual Workshop on Descriptional Complexity of Formal Systems (2010, August)Under some mild assumptions, we study the state complexity of the trim minimal automaton accepting the greedy representations of the multiples of m>=2 for a wide class of linear numeration systems. As an ... [more ▼]Under some mild assumptions, we study the state complexity of the trim minimal automaton accepting the greedy representations of the multiples of m>=2 for a wide class of linear numeration systems. As an example, the number of states of the trim minimal automaton accepting the greedy representations of mN in the Fibonacci system is exactly 2m^2. [less ▲]Detailed reference viewed: 100 (19 ULiège) Structure of the minimal automaton of a numeration languageCharlier, Emilie ; Rampersad, Narad ; Rigo, Michel et alin Actes de LaCIM 2010 (2010, August)We study the structure of automata accepting the greedy representations of N in a wide class of numeration systems. We describe the conditions under which such automata can have more than one strongly ... [more ▼]We study the structure of automata accepting the greedy representations of N in a wide class of numeration systems. We describe the conditions under which such automata can have more than one strongly connected component and the form of any such additional components. Our characterization applies, in particular, to any automaton arising from a Bertrand numeration system. Furthermore, we show that for any automaton A arising from a system with a dominant root beta>1, there is a morphism mapping A onto the automaton arising from the Bertrand system associated with the number beta. [less ▲]Detailed reference viewed: 133 (20 ULiège) Representing real numbers in a generalized numeration systemCharlier, Emilie Conference (2010, June)We show how to represent an interval of real numbers in an abstract numeration system built on a language that is not necessarily regular. As an application, we consider representations of real numbers ... [more ▼]We show how to represent an interval of real numbers in an abstract numeration system built on a language that is not necessarily regular. As an application, we consider representations of real numbers using the Dyck language. We also show that our framework can be applied to the rational base numeration systems. [less ▲]Detailed reference viewed: 11 (3 ULiège) Structure of the minimal automaton of a numeration language and applications to state complexityCharlier, Emilie ; Rampersad, Narad ; Rigo, Michel et alin Actes des Journées Montoises d'Informatique Théorique (2010)We study the structure of automata accepting the greedy representations of N in a wide class of numeration systems. We describe the conditions under which such automata can have more than one strongly ... [more ▼]We study the structure of automata accepting the greedy representations of N in a wide class of numeration systems. We describe the conditions under which such automata can have more than one strongly connected component and the form of any such additional components. Our characterization applies, in particular, to any automaton arising from a Bertrand numeration system. Furthermore, we show that for any automaton A arising from a system with a dominant root > 1, there is a morphism mapping A onto the automaton arising from the Bertrand system associated with the number . Under some mild assumptions, we also study the state complexity of the trim minimal automaton accepting the greedy representations of the multiples of m>=2 for a wide class of linear numeration systems. As an example, the number of states of the trim minimal automaton accepting the greedy representations of mN in the Fibonacci system is exactly 2m^2. [less ▲]Detailed reference viewed: 69 (9 ULiège) Multidimensional generalized automatic sequences and shape-symmetric morphic wordsCharlier, Emilie ; Kärki, Tomi; Rigo, Michel in Discrete Mathematics (2010), 310An infinite word is S-automatic if, for all n>=0, its (n+1)st letter is the output of a deterministic automaton fed with the representation of n in the numeration system S. In this paper, we consider an ... [more ▼]An infinite word is S-automatic if, for all n>=0, its (n+1)st letter is the output of a deterministic automaton fed with the representation of n in the numeration system S. In this paper, we consider an analogous definition in a multidimensional setting and study its relation to the shapesymmetric infinite words introduced by Arnaud Maes. More precisely, for d>1, we show that a multidimensional infinite word x over a finite alphabet is S-automatic for some abstract numeration system S built on a regular language containing the empty word if and only if x is the image by a coding of a shape-symmetric infinite word. [less ▲]Detailed reference viewed: 82 (17 ULiège) Abstract Numeration Systems : Recognizability, Decidability, Multidimensional S-Automatic Words, and Real NumbersCharlier, Emilie Doctoral thesis (2009)In this dissertation we study and we solve several questions regarding abstract numeration systems. Each particular problem is the focus of a chapter. The first problem concerns the study of the ... [more ▼]In this dissertation we study and we solve several questions regarding abstract numeration systems. Each particular problem is the focus of a chapter. The first problem concerns the study of the preservation of recognizability under multiplication by a constant in abstract numeration systems built on polynomial regular languages. The second is a decidability problem, which has been already studied notably by J. Honkala and A. Muchnik and which is studied here for two new cases: the linear positional numeration systems and the abstract numeration systems. Next, we focus on the extension to the multidimensional setting of a result of A. Maes and M. Rigo regarding S-automatic infinite words. Finally, we propose a formalism to represent real numbers in the general framework of abstract numeration systems built on languages that are not necessarily regular. We end by a list of open questions in the continuation of the present work. [less ▲]Detailed reference viewed: 205 (46 ULiège) A characterization of multidimensional S-automatic sequencesCharlier, Emilie ; Kärki, Tomi ; Rigo, Michel in Actes des rencontres du CIRM, 1 (2009)An infinite word is S-automatic if, for all n ≥ 0, its (n + 1)st letter is the output of a deterministic automaton fed with the representation of n in the considered numeration system S. In this extended ... [more ▼]An infinite word is S-automatic if, for all n ≥ 0, its (n + 1)st letter is the output of a deterministic automaton fed with the representation of n in the considered numeration system S. In this extended abstract, we consider an analogous definition in a multidimensional setting and present the connection to the shape-symmetric infinite words introduced by Arnaud Maes. More precisely, for d ≥ 2, we state that a multidimensional infinite word x : N^d → \Sigma over a finite alphabet \Sigma is S-automatic for some abstract numeration system S built on a regular language containing the empty word if and only if x is the image by a coding of a shape-symmetric infinite word. [less ▲]Detailed reference viewed: 47 (16 ULiège) Multidimensional generalized automatic sequences and shape-symmetric morphic wordsCharlier, Emilie ; Kärki, Tomi; Rigo, Michel in Proceedings of AutoMathA (2009)An infinite word is S-automatic if, for all n ≥ 0, its (n + 1)st letter is the output of a deterministic automaton fed with the representation of n in the considered numeration system S. In this paper, we ... [more ▼]An infinite word is S-automatic if, for all n ≥ 0, its (n + 1)st letter is the output of a deterministic automaton fed with the representation of n in the considered numeration system S. In this paper, we consider an analogous definition in a multidimensional setting and study the relationship with the shape-symmetric infinite words as introduced by Arnaud Maes. Precisely, for d ≥ 2, we show that a multidimensional infinite word x : N^d → Σ over a finite alphabet Σ is S-automatic for some abstract numeration system S built on a regular language containing the empty word if and only if x is the image by a coding of a shape-symmetric infinite word. [less ▲]Detailed reference viewed: 20 (3 ULiège) A Decision Problem for Ultimately Periodic Sets in Non-standard Numeration SystemsBell, Jason; Charlier, Emilie ; Fraenkel, Aviezri et alin International Journal of Algebra & Computation (2009), 19Consider a non-standard numeration system like the one built over the Fibonacci sequence where nonnegative integers are represented by words over {0,1} without two consecutive 1. Given a set X of integers ... [more ▼]Consider a non-standard numeration system like the one built over the Fibonacci sequence where nonnegative integers are represented by words over {0,1} without two consecutive 1. Given a set X of integers such that the language of their greedy representations in this system is accepted by a finite automaton, we consider the problem of deciding whether or not X is a finite union of arithmetic progressions. We obtain a decision procedure for this problem, under some hypothesis about the considered numeration system. In a second part, we obtain an analogous decision result for a particular class of abstract numeration systems built on an infinite regular language. [less ▲]Detailed reference viewed: 105 (31 ULiège) A decision problem for ultimately periodic sets in non-standard numeration systemsCharlier, Emilie Scientific conference (2008, December)Given a linear numeration system U and a set X (include in N) such that repU(X) is recognized by a (deterministic) finite automaton. Is it decidable whether or not X is ultimately periodic, i.e., whether ... [more ▼]Given a linear numeration system U and a set X (include in N) such that repU(X) is recognized by a (deterministic) finite automaton. Is it decidable whether or not X is ultimately periodic, i.e., whether or not X is a finite union of arithmetic progressions? Honkala showed that this problem turns out to be decidable for the usual b-ary numeration system (b greater than 2) defined by U_n = bU_{n-1} for n greater than 1 and U_0 = 1. In this work, we give a decision procedure for this problem for a large class of linear numeration systems. [less ▲]Detailed reference viewed: 17 (1 ULiège) A decision problem for ultimately periodic sets in non-standard numeration systemsCharlier, Emilie Conference (2008, May)We consider the following decidability problem: Given a linear numeration system U and a set X ⊆ N such that rep_U(X) is recognized by a (deterministic) finite automaton. Is it decidable whether or not X ... [more ▼]We consider the following decidability problem: Given a linear numeration system U and a set X ⊆ N such that rep_U(X) is recognized by a (deterministic) finite automaton. Is it decidable whether or not X is ultimately periodic, i.e., whether or not X is a finite union of arithmetic progressions? In this work, we give a decision procedure for this problem whenever U is a linear numeration system such that N is U -recognizable and satisfying a relation of the form U_{i+k} = a_1 U_{i+k−1} + · · · + a_k U_i with a_k = ±1 (the main reason for this assumption is that 1 and −1 are the only two integers invertible modulo n for all n ≥ 2). [less ▲]Detailed reference viewed: 22 (4 ULiège) Systèmes de numérationCharlier, Emilie Scientific conference (2008, February)Dans cet exposé, je propose une introduction aux systèmes de numération en général : bases entières, numérations linéaires, numérations abstraites. Je donnerai les premiers résultats et attirerai l ... [more ▼]Dans cet exposé, je propose une introduction aux systèmes de numération en général : bases entières, numérations linéaires, numérations abstraites. Je donnerai les premiers résultats et attirerai l'attention sur différents axes de recherche possibles. [less ▲]Detailed reference viewed: 10 (1 ULiège) Abstract numeration systems on bounded languages and multiplication by a constantCharlier, Emilie ; Rigo, Michel ; Steiner, Wolfgangin INTEGERS: Electronic Journal of Combinatorial Number Theory (2008), 8(1-A35), 1-19A set of integers is $S$-recognizable in an abstract numeration system $S$ if the language made up of the representations of its elements is accepted by a finite automaton. For abstract numeration systems ... [more ▼]A set of integers is $S$-recognizable in an abstract numeration system $S$ if the language made up of the representations of its elements is accepted by a finite automaton. For abstract numeration systems built over bounded languages with at least three letters, we show that multiplication by an integer $\lambda\ge2$ does not preserve $S$-recognizability, meaning that there always exists a $S$-recognizable set $X$ such that $\lambda X$ is not $S$-recognizable. The main tool is a bijection between the representation of an integer over a bounded language and its decomposition as a sum of binomial coefficients with certain properties, the so-called combinatorial numeration system. [less ▲]Detailed reference viewed: 42 (7 ULiège) A decision problem for ultimately periodic sets in non-standard numeration systemsCharlier, Emilie ; Rigo, Michel in Actes des Journées Montoises d'Informatique Théorique (2008)Consider a non-standard numeration system like the one built over the Fibonacci sequence where nonnegative integers are represented by words over {0, 1} without two consecutive 1. Given a set X of ... [more ▼]Consider a non-standard numeration system like the one built over the Fibonacci sequence where nonnegative integers are represented by words over {0, 1} without two consecutive 1. Given a set X of integers such that the language of their greedy representations in this system is accepted by a finite automaton, we consider the problem of deciding whether or not X is a finite union of arithmetic progressions. We obtain a decision procedure under some hypothesis about the considered numeration system. In a second part, we obtain an analogous decision result for a particular class of abstract numeration systems built on an infinite regular language. [less ▲]Detailed reference viewed: 25 (3 ULiège) A Decision Problem for Ultimately Periodic Sets in Non-standard Numeration SystemsCharlier, Emilie ; Rigo, Michel in Lecture Notes in Computer Science (2008), 5162Consider a non-standard numeration system like the one built over the Fibonacci sequence where nonnegative integers are represented by words over {0, 1} without two consecutive 1. Given a set X of ... [more ▼]Consider a non-standard numeration system like the one built over the Fibonacci sequence where nonnegative integers are represented by words over {0, 1} without two consecutive 1. Given a set X of integers such that the language of their greedy representations in this system is accepted by a finite automaton, we consider the problem of deciding whether or not X is a finite union of arithmetic progressions. We obtain a decision procedure under some hypothesis about the considered numeration system. In a second part, we obtain an analogous decision result for a particular class of abstract numeration systems built on an infinite regular language. [less ▲]Detailed reference viewed: 30 (13 ULiège) Abstract numeration systemsCharlier, Emilie Conference (2007, May)In this talk, I will introduce abstract numeration systems in general and present some results I have regarding operation preserving regularity. In particular, I will focus on multiplication by a constant.Detailed reference viewed: 12 (1 ULiège) Structural properties of bounded languages with respect to multiplication by a constantCharlier, Emilie Conference (2007, April)Generalizations of positional number systems in which N is recognizable by finite automata are obtained by describing an arbitrary infinite regular language according to the genealogical ordering. More ... [more ▼]Generalizations of positional number systems in which N is recognizable by finite automata are obtained by describing an arbitrary infinite regular language according to the genealogical ordering. More precisely, an abstract numeration system is a triple S = (L, Σ, <) where L is an infinite language over the totally ordered alphabet (Σ, <). Enumerating the elements of L genealogically with respect to < leads to a one-to-one map rS from N onto L. To any natural number n, it assigns the (n + 1)th word of L, its S-representation, while the inverse map valS sends any word belonging to L onto its numerical value. A subset X is said to be S-recognizable if rS (X) is a regular subset of L. We study the preservation of recognizability of a set of integers after multiplication by a constant for abstract numeration systems built over a bounded language. [less ▲]Detailed reference viewed: 13 (4 ULiège) Abstract numeration systems and recognizabilityCharlier, Emilie Conference (2007, January)In this talk, I will present some results concerning multiplication by a constant in an abstract numeration system built on a bounded language. More precisely, we will show that this operation does not ... [more ▼]In this talk, I will present some results concerning multiplication by a constant in an abstract numeration system built on a bounded language. More precisely, we will show that this operation does not preserve regularity, and therefore cannot be computed by a finite automaton. [less ▲]Detailed reference viewed: 11 (1 ULiège)     1 2 3 4


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# Math Help - Poker math question (algebra)

1. ## Poker math question (algebra)

Our opponent bets $70 into a$100 pot on the river. How often to we need to win to make the call break even?

The answer given was $170(X) -$70(1-X) = 0, so X = 0.292 or 29.2%

2. ## Re: Poker math question (algebra)

Never mind, I think I've got it.

70 to call so pot will be 240.

70/240 = 0.2916

29.2%

3. ## Re: Poker math question (algebra)

Anyone know how I'd get the algebraic answer though, as in line 2 of my opening post?

4. ## Re: Poker math question (algebra)

Are you sure you have copied the problem correctly? It should be "us" who bet $70, not "our opponent". What they are saying is that if you win "X" of the time, you will lose 1- X of the time. When you win you win$170 dollars. When you lose, you lose \$70 so in the long run you will win 170X dollars and lose 70(1- X) dollars. "To break even" means you neither lose nor win any money: 170X- 70(1- X)= 0. That is the same as 170X- 70+ 70X= 240X- 70= 0 so 240X= 70 and X= 70/240= 7/24= .2916666 or about 29.2%.

5. ## Re: Poker math question (algebra)

Thanks for replying. The problem was definitely posed saying "Our opponent bets 70 into 100 on the river"

That aside though, how do I learn to work this stuff out myself? What mathematical topic is it?

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In YiFengEDMS/simPM: SIMulation-based power analysis for Planned Missing designs

knitr::opts_chunk$set( collapse = TRUE, comment = "#>" )  In this vignette we will demonstrate how to use simPM to search for an optimal PHPM design for a longitudinal research study that employs a linear latent growth model (LGM). Research Scenario In this hypothetical scenario, a researcher (Dr. X) is interested in studying the longitudinal growth of adolescents' self-esteem. Dr. X has proposed a longitudinal study that is expected to extend over 4 years. Participants will be assessed on self-report self-esteem annually. The data will be analyzed using a linear LGM, as seen in the following diagram. Because the goal of the study is to examine the typical growth trajectory as well as the inter-individual trajectory variability, the model parameters of focal interest are the mean and variance of both the latent intercept and slope (shown in red). Very unfortunately, after completing the first wave of data collection, due to various external reasons the sponsor decides to implement a 30% reduction in funding for remaining three waves. Dr. X wishes to continue the study with a new data collection plan. She decides to use simPM to find a design that yields sufficient power but costs no more than the reduced budget. knitr::include_graphics('images/linear_lgm.png')  Spcify the Population and Analysis Model simPM searches for an optimal design based on power analysis using Monte Carlo simulations. To implement power analysis, we first need to supply a population data generating model and an analysis model. The easiest way to specify the population model and analysis model is to use the lavaan model syntax. For this linear LGM example, the population model is specified as the follows, assuming Dr. X has made an informed decision about the population model and parameter values based on substantive thoery and past research. popModel <- ' #----- loadings -----# i=~1*se1+1*se2+1*se3+1*se4 s=~0*se1+1*se2+2*se3+3*se4 #----- mean structure ----# se1~0*1 se2~0*1 se3~0*1 se4~0*1 i~2.983*1 s~0.086*1 #---- residual variances ----# se1~~0.071*se1 se2~~0.034*se2 se3~~0.067*se3 se4~~0.025*se4 #---- variance-covariance strucutre of latent variables ----# i~~0.268*i+(-0.039)*s s~~0.023*s '  The analysis model is specified as the same linear LGM with freely estimated model parameters: analyzeModel <- ' #----- loadings -----# i=~1*se1+1*se2+1*se3+1*se4 s=~0*se1+1*se2+2*se3+3*se4 #----- mean structure ----# se1~0*1 se2~0*1 se3~0*1 se4~0*1 i~1 s~1 #---- residual variances ----# se1~~se1 se2~~se2 se3~~se3 se4~~se4 #---- variance-covariance strucutre of latent variables ----# i~~i+s s~~s '  Search for an Optimal Wave-level Design We can use the main function simPM() to search for an optimal wave-level missing design. For simPM() to work properly, we need to supply the relevant information about this longitudinal study. By running the following code, simPM will automatically map out all the possible PHPM designs, run power analysis for each plausible design, and output the optimal design. wave.ex1=simPM(popModel = popModel, #supply the population model using lavaan language analyzeModel = analyzeModel, #supply the analysis model using lavaan language VarNAMES = c("se1","se2","se3","se4"), #the observed variable names Time = 4, #total number of waves Time.complete = 1, #number of waves completed before funding cut occurs k = 1, #number of observed variables collected at each wave pc = 0.2, #percentage of participants to provide complete data after funding cut pd = 0, #percentage of participants to provide no data after funding cut costmx = c(5,10,15), #unit cost of each data point at the following waves n = 323, #original sample size nreps = 1000, #number of replications for simulation focal.param = c("i~1","s~1","i~~i","s~~s"), #specify the focal parameters complete.wave = NULL, #specify any future wave/variables that need complete data eval.budget = T, #whether or not there is a budget restriction rm.budget = 30*323*0.7, #the amount of remaining budget distal.var = NULL, #specify any distal variables that are not subject to PM seed = 12345, #random seed engine = "l", #use lavaan to fit the models methods = "wave") #type of PHPM designs, "wave" indicates wave-level missing  More specifically: • VarNAMES = c("se1","se2","se3","se4"): The observed variables collected in this study are named se1, se2, se3, and se4. • Time = 4: The study has 4 waves of data collection in total. • Time.complete = 1: One wave of data collection has been completed before funding cut occurs. • k = 1: Only one observed variable is collected at each wave. • pc = 0.2: Twenty percent of the participants are assigned to provide complete data for future waves after funding cut. • pd = 0: Zero percent of the participants are assigned to drop from the study. • costmx = c(5,10,15): The unit cost of one data point is \$5 at wave 2, \$10 at wave 3, and \$15 at wave 4.
• n = 323: The original sample size planned was 323.
• nreps = 1000: The program will run 1000 replications for Monte Carlo simulation (for each plausible design).
• focal.param = c("i~1","s~1","i~~i","s~~s"): The focal parameters of interest are the mean and variance of the latent intercept and slope.
• complete.wave = NULL: No future waves are by design to have complete data from each participant.
• eval.budget = T: Yes, there is a budget restriction.
• rm.budget = 30*323*0.7: After the funding cut, the researcher will have $\$6,783(=30\times323\times0.7)$to support the future waves of data collection • distal.var = NULL: There are no distal variables in the model that are not subject to repeated measures (and thus not considered for PHPM). • engine = "l": Model fitted using lavaan. • methods = "wave": Search for wave-level missing designs. Summarize the Result setwd("C:/Users/yifeng94/Desktop/simPM/simPM-git/examples") load("wave.ex1_r1.rda") library(simPM)  To view a summary of the results, we can use the summary.simpm() function. It prints out the comparison among all the plausible wave-level missing designs (the comparison is made with regard to the focal parameter who has the lowest empirical power). The function will also print the optimal design that was selected, the details about the focal parameters for the selected optimal design, the missing data pattern for the selected optimal PHPM design, and the proportion as well as the number of participants assigned to each unqie missing data pattern. summary(wave.ex1)  For this example, there is only one possible wave-level PHPM design given the budget constraints. Therefore, the program has run simulations only for this one possible design. This design costs \$4,530, which is below the reduced available budget.

[1] "=================results summary================"
convergence.rate weakest.param.name weakest.para.power cost.design miss.waves
1             0.92               s~~s              0.999        4530          2
[1] "=================Optimal design================="
convergence.rate weakest.param.name weakest.para.power cost.design miss.waves
1             0.92               s~~s              0.999        4530          2

With this design, 20% of the participants are assigned to provide complete data across all the future waves of data collection. The rest 80% of the participants are randomly assigned to one of the three unique missing data patterns ($n=86$ in each pattern). In the pattern matrix, 1 indicates planned missingness and 0 indicates planned complete data.

[1] "=================Optimal patterns==============="
se1 se2 se3 se4
0   1   1   0
0   1   0   1
0   0   1   1
completers   0   0   0   0
[1] "=================Optimal probs=================="
[1] 0.266667 0.266667 0.266667 0.200000
[1] "=================Optimal ns===================="
[1] 86 86 86 65

Over 1000 replications, this design yields an empirical power of 0.999 for testing the slope variance $\sigma^2_\beta$; the statistical power is 1 for testing the mean intercept ($\mu_\alpha$), the mean slope ($\mu_\beta$), and the intercept variance ($\sigma^2_\alpha$).

[1] "=================Optimal design for focal parameters================="
Estimate Average Estimate SD  Average SE Power (Not equal 0)   Std Est   Std Est SD
i~1        2.98293751 0.031715239 0.031616120               1.000 5.8125191 3.214384e-01
s~1        0.08626832 0.012315538 0.011890850               1.000 0.5821286 1.071983e-01
i~~i       0.26565608 0.028395191 0.027694967               1.000 1.0000000 1.479881e-16
s~~s       0.02275121 0.004702874 0.004540174               0.999 1.0000000 1.476542e-16
Std Ave SE Average Param  Average Bias Coverage Average FMI1    SD FMI1
i~1   0.3109336         2.983 -6.248508e-05    0.945   0.06909154 0.02634767
s~1   0.1017555         0.086  2.683187e-04    0.939   0.33360543 0.03811522
i~~i  0.0000000         0.268 -2.343916e-03    0.935   0.25362176 0.04437375
s~~s  0.0000000         0.023 -2.487868e-04    0.939   0.62234904 0.04767489

To view more details of the optimal PHPM design, we can use the following code, which will give us more detailed information about the simulation results for this selected PHPM design.

summary(wave.ex1\$opt.output)

Visualize the Optimal Design

To visualize the missing data patterns of the optimal PHPM design, we can use the plotPM() function. It will plot the missing data pattern matrix so people can have a more intuitive understanding of the optimal design that was selected. In this plot, each row represents a unique missing data pattern. Each column represents an observed variable. The number of participants assigned to each missing data pattern is also labeled.

In this example, we can see that 65 participants are assigned to provide complete data over the future waves of data collection, while the rest of the participants are assigned to one of the three missing data patterns. For instance, there are 86 participants who are randomly picked to NOT provide data in wave 2 and wave 3 (the first row of the plot); Another 86 participants are randomly picked to NOT provide data in wave 2 and wave 4 (the second row of the plot).

plotPM(wave.ex1)

YiFengEDMS/simPM documentation built on Dec. 31, 2019, 8:54 a.m.


text:
# In Unity - Move a GameObject at Animator State

I want to move one of my GameObject to a different vector 3 position, when animator transit to a new state. How do I do it? Also there shouldn't be any delay.

• Can you show some code of what you've tried? Nov 24, 2016 at 11:38

You Don't need to moving via animating. You can simply make a method that first change the animation state and then move object using Translate method( for instant transition) and MoveTowards or some other methods. Something like this :

Public myMethod (){
animator.set...();
transform.translate...
}

And whenever you call myMethod you have two behaviors together.

• Thanx this gave me a good hint to use a Behaviour, So found a solution, posting below Nov 28, 2016 at 0:43

This is the solution I came up with, In my Animator state I added a behaviour script, that moves the object before the animation starts,

Script is a very simple C# script:

using UnityEngine;
using System.Collections;

public class BehaviorMoveGameObject : StateMachineBehaviour {

public float Position_X;
public float Position_Y;
public float Position_Z;

// OnStateEnter is called when a transition starts and the state machine  starts to evaluate this state
override public void OnStateEnter (Animator animator, AnimatorStateInfo stateInfo, int layerIndex)
{

animator.gameObject.transform.position = new Vector3 (Position_X, Position_Y, Position_Z);

}

}


text:
# Schrodinger solution to hamilton-jacobi

Identity
The Hamilton-Jacobi equation

$$\frac{\partial W}{\partial t}+\frac{1}{2m}\left[\left(\frac{\partial W}{\partial x}\right)^2+\left(\frac{\partial W}{\partial y}\right)^2+\left(\frac{\partial W}{\partial z}\right)^2\right] + V(x,y,z) = 0$$

Can be re-expressed as $$|\nabla W| = \sqrt{2m(E-V)}$$ by taking $$W = -Et+S(x,y,z)$$

Schrodinger says that if we think of the level curves of W, and assign an arbitrary curve the value $$W_0$$, that we can take a normal to that paticular level curve (spanning $$W_0+dW$$) to be":

$$dn = \frac{dW_0}{\sqrt{2m(E-V)}}$$

(In other words, $$\frac{dW_0}{dn} = |\nabla W|$$)

Where does this come from? How do we know the normal differential has this value?

thanks

Isn't it just $$|n| = |\nabla W|$$??


text:
## Continuous approximations, codifferentiable functions and minimization methods.(English)Zbl 0973.49013

Demyanov, V. (ed.) et al., Quasidifferentiability and related topics. Dedicated to Prof. Franco Giannessi on his 65th birthday and to Prof. Diethard Pallaschke on his 60th birthday. Dordrecht: Kluwer Academic Publishers. Nonconvex Optim. Appl. 43, 361-391 (2000).
The function $$f^{\odot}: \mathbb{R}^n\times \mathbb{R}^n\to \mathbb{R}$$ is called a first-order approximation of the (nonsmooth) function $$f: \mathbb{R}^n\to \mathbb{R}$$ if for all $$x\in \mathbb{R}^n$$ and $$d\in\mathbb{R}^n$$ $f(x+ d)- f(x)= f^{\odot}(x, d)+ o_x(d),\quad\text{where }\lim_{\alpha\downarrow 0} {o_x(\alpha d)\over \alpha}= 0.$ Clearly, if $$f^{\odot}(x,d)$$ is positively homogeneous, then $$f^{\odot}(x,d)$$ coincides with the directional derivative $$f'(x,d)$$ and topological properties of $$f^{\odot}(\cdot,d)$$ are closely connected with algebraic properties of $$f^{\odot}(x, \cdot)$$. So the directional derivative $$f'(x,\cdot)$$ is linear (resp. sublinear) if $$f'(\cdot,d)$$ is continuous (resp. upper semicontinuous). Hence, for a nonsmooth function the directional derivative can not be continuous with respect to $$x$$.
To get continuous first-order approximations of nonsmooth functions (which are important especially for numerical methods) the author uses approximations which are not homogeneous. According to Demyanov, the function $$f$$ is called to be codifferentiable if there exists a pair of convex compact sets $$\underline df(x),\overline df(x)\subset \mathbb{R}^{n+1}$$ (the codifferential of $$f$$) such that $f(x+ d)- f(x)= \max_{(a,u)\in \underline df(x)} [a+\langle u,d\rangle]+ \min_{(b,w)\in\overline df(x)} [b+ \langle w,d\rangle]+ o_x(d).$ Hence, codifferentiable functions admit first-order approximations $$f^{\odot}(x, d)$$ which are difference convex with respect to $$d$$. The class of codifferentiable functions coincides with the class of quasidifferentiable functions. However, in contrast to quasidifferentiability there exists a large class of nonsmooth functions which allow Hausdorff-continuous codifferentials.
In the paper, the author summarizes calculus rules for (continuously) codifferentiable functions and provides applications to nonsmooth optimization problems. The second part of the paper is devoted to the extension of the concept of codifferentiability to mappings defined between Banach spaces.
For the entire collection see [Zbl 0949.00047].

### MSC:

 49J52 Nonsmooth analysis 90C26 Nonconvex programming, global optimization


text:
# Cohomological methods in Group Theory

Friday, 23rd September 2022, 1pm – 5pm, Senate House, room 102 (Senate House University of London, Malet St, London WC1E 7HU). Local organiser: Brita Nucinkis

The meeting will take place in person at University of London (Central London Campus).

## Speakers

• Paula Macedo Lins de Araujo (University of Lincoln), Soluble matrix groups and $R_\infty$ property
• Yuri Santos Rego (University of Magdeburg), Cohomological finiteness length of matrix groups
• Pavel Zalesski (University of Brasilia), Splitting of pro-p groups (as an amalgam or HNN)

To register for the event and to receive the talk links, please email Brita Nucinkis (Brita.Nucinkis@rhul.ac.uk).

The FCG Research Group is supported by an LMS Joint Research Groups in the UK Scheme 3 grant. Limited funding is available for PhD students, allocated on a first come first served basis.

For UK-based mathematicians with caring duties the LMS has a Caring Supplementary Grant scheme which allows participants of meetings like ours to apply for help covering caring costs.

## Abstracts

Paula Macedo Lins de Araujo (University of Lincoln), Soluble matrix groups and $R_\infty$ property

A group automorphism $\varphi: \Gamma \to \Gamma$ induces the action $g\cdot x= gx\varphi(g)^{-1}$ on $\Gamma$. The orbits of such action are called Reidemeister classes.

In the past few years, the sizes of such classes have been intensively investigated. One of the main goals in the area is to classify groups where all classes are infinite. Such groups are said to satisfy the $R_\infty$ property.

Although much is known about Reidemeister classes of nilpotent or polycyclic groups, Reidemeister classes of soluble groups in general have not been as intensively studied, so that there are still has many open questions to be explored.

In this talk, we will discuss the relation of Reidemeister classes with non-abelian cohomology. We also show conditions for certain soluble groups to have the $R_\infty$

This talk is based on joint works with K. Dekimpe and Y. Santos Rego.

Yuri Santos Rego (University of Magdeburg), Cohomological finiteness length of matrix groups

Since many groups occurring naturally turn out to be linear (e.g., surface groups, Coxeter groups, crystallographic groups), the family of groups defined by matrices has rich (co)homological properties. The cohomological finiteness length is a particularly useful quasi-isometry invariant, though computing it for prominent matrix groups is an ongoing challenge.

In this talk we shall recall the definition and important properties of the cohomological finiteness length, going through well-known examples. Shifting focus, we shall discuss the state of knowledge for classical matrix groups over integral domains and present some recent results in this direction.

Pavel Zalesski (University of Brasilia), Splitting of pro-p groups (as an amalgam or HNN)

I shall talk about Stallings type results of splittings of pro-p groups as an amalgamated free pro-p product or a pro-p HNN-extension as well as some other aspects of such splittings.


text:
Trying to find an angle in lines layed on top of a circle

1. Jul 28, 2012

s3a

1. The problem statement, all variables and given/known data
The problem is attached as TheProblem.jpg and the answer is A.

2. Relevant equations
Geometry rules.

3. The attempt at a solution
The triangle which has angles of 30deg and 10deg also has an angle of 180deg-30deg-10deg = 140deg and the other side of the line intersection “scissor” is also 140deg. The two equivalent angles on the other part of the line intersection “scissor” are (360deg-2*140deg)/2 = 40deg. I don't know if what I did so far is even useful nor do I know how to proceed from here.

Any help would be greatly appreciated!

Attached Files:

• TheProblem.jpg
File size:
15.3 KB
Views:
78
2. Jul 28, 2012

Villyer

First try and identify what arcs you need to know the measure of to find angle ACE.
What formula are you going to ultimately use?

3. Jul 29, 2012

s3a

I'm really unsure but (1) arc AE and (2) comparing an angle ratio with an arc/circumference ratio?

Last edited: Jul 29, 2012
4. Jul 29, 2012

HallsofIvy

Have you learned "If AB and CD are lines intersecting inside a circle, then the angle between them is the average of the two arcs they make on the circle"? That is the theorem you need.

5. Jul 30, 2012

s3a

HallsofIvy, did you mean "difference" instead of "average"? Because, if you did, then I get the correct answer by doing:

angle A0E = 2 * angle ABE = 2 * 30deg = 60deg

then

angle ACE = 1/2 * (60-10) deg = 25deg

6. Jul 30, 2012

Curious3141

Consider the chord BD (and the minor arc BD). What can you say about the relationship between the angles BOD and BED?

That should take you most of the way.

7. Jul 31, 2012

HallsofIvy

Well, the rule I was thinking of requires that when two lines intersecting a circle come from outside the circle, the arc it cuts is considered negative. The lines BA and BE intersect an arc of measure 0 (at B) and arc AE. The angle is 30 degrees so we have (AE+ 0)/2= 30 so arc AE has measure 2(30)= 60 degrees.

Arc AD is intercepted by lines BO and DO. Of course, the measure of an angle is defined by the central angle it intercepts so it has measure 10 degrees. (Of course, the other arc those two lines intercept would be 10 degrees also so "average" still works.)

That is, lines CA and CE intercept the circle in arcs AE and BD. They come to arc AE from outside the outside so we consider that arc measure negative: the measure of the angle is (-10+ 60)/2= 25 degrees.


text:
# MGF of inverse discrete random variable

The following question is straightforward to show with Markov's Inequality:

Let $X_n$ be uniformly distributed on the set {1, 2, ..., n}, and let $Y_n = 1/X_n$. Prove that $Y_n \overset{p}{\rightarrow} 0$.

For practice, I also wanted to use MGFs (on the justification $Z_n\overset{p}{\rightarrow} c \iff Z_n \overset{d}{\rightarrow} c$ where $c$ is a constant). It follows that $M_{Y_n}(t) = \frac{1}{n} \sum_{x=1}^n e^{t/x}$, but when I do the limit by hand I get 0. I also get 0 using Mathematica:

Limit[ Sum[  (1/n) Exp[t/x]   , {x, 1, n}], n -> Infinity]
0

Clearly these are both "wrong" because the MGF of a degenerate random variable equal to 0 with probability 1 is "1", and so that must be the "proper" limit.

The MGF has to only exist in a neighborhood of 0 for $t$, and clearly at $t = 0$ the limit is 1 (but not for any specific but arbitrarily small $t$).

My only thoughts are that I have the MGF wrong itself or that there's something subtle happening with the limit of the arithmetic mean of infinite terms close to 1. Any thoughts would be appreciated!

Edit: Adding a note that my Mathematica version is 11.3, primarily for reference if it helps someone in the future.

• Mathematica 9.0.1.0 does not make the same error with the limit. – whuber Jul 28 '18 at 20:46

It looks like the mgf is correct, because by definition

$$M_{Y_n}(t) = E[\exp(t Y_n)] = \sum_{x=1}^n \exp(t / x) \Pr(X_n=x) = \frac{1}{n}\sum_{x=1}^n \exp(t/x).$$

Since $t$ is real, all these terms are positive. The arithmetic-geometric mean inequality implies

$$M_{Y_n}(t) \ge \left(\prod_{x=1}^n \exp(t/x)\right)^{1/n} = \exp\left(t H_n/n\right)$$

where I have written $H_n=1+1/2+\cdots + 1/n$ for the $n^\text{th}$ Harmonic number. As is well known (and easy to show), $H_n/n\to 0$ as $n$ grows large. The continuity of $\exp$ then implies the right hand side of $(*)$ approaches $\exp(t0)=1$ in the limit. That is,

$$\lim_{n\to\infty}M_{Y_n}(t) \ge 1.\tag{*}$$

On the other hand, consider any real $t$ and select an arbitrary $\varepsilon \gt 0.$ For all integers $n \gt |t| / \log(1+\varepsilon),$ $\exp(t/n) \lt 1 + \varepsilon.$ Let $N \ge 1$ be an integer and break the sum for $M_{Y_{N+n}}(t)$ into two parts,

\eqalign{ M_{Y_{N+n}}(t) &= \frac{1}{N+n} \sum_{x=1}^n \exp(t/x) + \frac{1}{N+n} \sum_{x=n+1}^{N+n} \exp(t/x) \\ &= \frac{n}{N+n} M_{Y_n}(t) + \frac{1}{N+n} \sum_{x=n+1}^{N+n} \exp(t/x) \\ &\lt \frac{n}{N+n} M_{Y_n}(t) + \frac{1}{N+n} \sum_{x=n+1}^{N+n}(1+\varepsilon) \\ &= \frac{n}{N+n} M_{Y_n}(t) + \frac{N}{N+n}(1 + \varepsilon). }

As $N$ grows large (still keeping $t,$ $\varepsilon,$ and $n$ fixed), the first term converges to $0$ while the second converges to $1 + \varepsilon,$ establishing

$$\lim_{n\to\infty} M_{Y_n}(t) \le 1 + \varepsilon.\tag{**}$$

Since $\varepsilon$ is arbitrarily small, results $(*)$ and $(**)$ together show the limit of the mgf can only be the unit constant function.


text:
In an ac circuit, V and I are given by V = 100 sin (100 t) volts, $I=100\mathrm{sin}\text{\hspace{0.17em}}\left(100t+\frac{\pi }{3}\right)\text{\hspace{0.17em}}mA$. The power dissipated in circuit is

(1) 104 watt

(2) 10 watt

(3) 2.5 watt

(4) 5 watt

Concept Questions :-

Rms and average values
To view Explanation, Please buy any of the course from below.
High Yielding Test Series + Question Bank - NEET 2020

Difficulty Level:

The resistance of a coil for dc is in ohms. In ac, the impedance:

(1) Will remain the same

(2) Will increase

(3) Will decrease

(4) Will be zero

Concept Questions :-

AC vs DC
To view Explanation, Please buy any of the course from below.
High Yielding Test Series + Question Bank - NEET 2020

Difficulty Level:

A generator produces a voltage that is given by V = 240 sin 120 t, where t is in seconds. The frequency and r.m.s. voltage are

(1) 60 Hz and 240 V

(2) 19 Hz and 120 V

(3) 19 Hz and 170 V

(4) 754 Hz and 70 V

Concept Questions :-

Rms and average values
To view Explanation, Please buy any of the course from below.
High Yielding Test Series + Question Bank - NEET 2020

Difficulty Level:

The peak value of an alternating e.m.f. E is given by $E={E}_{0}\mathrm{cos}\omega \text{\hspace{0.17em}}t$ is 10 volts and its frequency is 50 Hz. At time $t=\frac{1}{600}sec$, the instantaneous e.m.f. is

(1) 10 V

(2) $5\sqrt{3}\text{\hspace{0.17em}}V$

(3) 5 V

(4) 1 V

Concept Questions :-

Different types of AC Circuits
To view Explanation, Please buy any of the course from below.
High Yielding Test Series + Question Bank - NEET 2020

Difficulty Level:

If a current I given by ${I}_{0}\mathrm{sin}\text{\hspace{0.17em}}\left(\omega \text{\hspace{0.17em}}t-\frac{\pi }{2}\right)$ flows in an ac circuit across which an ac potential of $E={E}_{0}\mathrm{sin}\omega \text{\hspace{0.17em}}t$ has been applied, then the power consumption P in the circuit will be

(1) $P=\frac{{E}_{0}{I}_{0}}{\sqrt{2}}$

(2) $P=\sqrt{2}{E}_{0}{I}_{0}$

(3) $P=\frac{{E}_{0}{I}_{0}}{2}$

(4) P = 0

Concept Questions :-

Different types of AC Circuits
To view Explanation, Please buy any of the course from below.
High Yielding Test Series + Question Bank - NEET 2020

Difficulty Level:

In an ac circuit, the instantaneous values of e.m.f. and current are e = 200 sin 314 t volt and $i=\mathrm{sin}\text{\hspace{0.17em}}\left(314t+\frac{\pi }{3}\right)$ ampere. The average power consumed in watt is

(1) 200

(2) 100

(3) 50

(4) 25

Concept Questions :-

Rms and average values
To view Explanation, Please buy any of the course from below.
High Yielding Test Series + Question Bank - NEET 2020

Difficulty Level:

An alternating current is given by the equation $i={i}_{1}\mathrm{cos}\omega \text{\hspace{0.17em}}t+{i}_{2}\mathrm{sin}\omega \text{\hspace{0.17em}}t$. The r.m.s. current is given by

(1) $\frac{1}{\sqrt{2}}\left({i}_{1}+{i}_{2}\right)$

(2) $\frac{1}{\sqrt{2}}{\left({i}_{i}+{i}_{2}\right)}^{2}$

(3) $\frac{1}{\sqrt{2}}{\left({i}_{1}^{2}+{i}_{2}^{2}\right)}^{1/2}$

(4) $\frac{1}{2}{\left({i}_{1}^{2}+{i}_{2}^{2}\right)}^{1/2}$

Concept Questions :-

Rms and average values
To view Explanation, Please buy any of the course from below.
High Yielding Test Series + Question Bank - NEET 2020

Difficulty Level:

In an ac circuit, the current is given by $i=5\mathrm{sin}\text{\hspace{0.17em}}\left(100\text{\hspace{0.17em}}t-\frac{\pi }{2}\right)$ and the ac potential is V = 200 sin(100t) volt. Then the power consumption is :

(1) 20 watts

(2) 40 watts

(3) 1000 watts

(4) 0 watt

Concept Questions :-

Different types of AC Circuits
To view Explanation, Please buy any of the course from below.
High Yielding Test Series + Question Bank - NEET 2020

Difficulty Level:

A resistance of 20 ohms is connected to a source of an alternating potential $V=220\mathrm{sin}\left(100\pi t\right)$. The time taken by the current to change from its peak value to r.m.s value is

(1) 0.2 sec

(2) 0.25 sec

(3) 25 × 10–3 sec

(4) 2.5 × 10–3 sec

Concept Questions :-

Different types of AC Circuits
To view Explanation, Please buy any of the course from below.
High Yielding Test Series + Question Bank - NEET 2020

Difficulty Level:

Voltage and current in an ac circuit are given by $V=5\mathrm{sin}\text{\hspace{0.17em}}\left(100\pi t-\frac{\pi }{6}\right)$ and $I=4\mathrm{sin}\text{\hspace{0.17em}}\left(100\pi t+\frac{\pi }{6}\right)$

(1) Voltage leads the current by 30°

(2) Current leads the voltage by 30°

(3) Current leads the voltage by 60°

(4) Voltage leads the current by 60°

Concept Questions :-

Different types of AC Circuits
To view Explanation, Please buy any of the course from below.
High Yielding Test Series + Question Bank - NEET 2020

Difficulty Level:


text:
Optical Theorem

1. Jan 5, 2010

david_clint

1. The problem statement, all variables and given/known data
Hi. For the question given (attachment) where does the factor of 2PI in the function for sigma come from in the first step because I don't get it in my working for the first step.

2. Relevant equations
see attachment

3. The attempt at a solution
I got sigma (without the 2PI) by changing variable to t =cos theta, thus integrating between minus and plus 1

and using m=n in the legendre polynomial,

so I am wondering if the 2PI came from integrating over the phi dependence as we are dealing with scattering from a radial potential?

I also need prodding in the right direction for the next step!

Attached Files:

• 14.JPG
File size:
25.9 KB
Views:
65
Last edited: Jan 5, 2010
2. Jan 6, 2010

Avodyne

Yes, the 2pi comes from integrating over phi, and so there should be a 2pi in front of the integral sign in the last equation.

3. Jan 6, 2010

Thanks:)


text:
# Angle Modulation MCQ || Angle Modulation Questions and Answers

1. In FM modulation, when the modulation index increases, the transmitted power is

1. Increased
2. Decreased
3. Unchanged
4. None of these

Explanation

The amplitude Ac is constant in a phase-modulated or a frequency-modulated signal. RF power does not depend upon the modulation index.

A general expression for a phase or frequency modulated signal is:

φ(t) = AcCos[ωct + (gKk, m(t))]

m(t) = the modulating signal

ωc = Carrier frequency

kk becomes kc for FM and kp for PM.

The average power (Pavg) is given by:

Pavg = A2c/2

We observe that the transmitted power is independent of the modulation index in case of FM.

2. Reactance modulator and varactor diode are used in the _____ method.

1. DSB –SC generation
2. DSB –SC reception
3. SSB generation
4. FM generation

Explanation

• Reactance modulators are used for the generation of frequency modulation (FM)
• These reactance modulators do not have very good frequency stability. But if it is to be used for broadcast applications, then it is must-have high-frequency stability. It can be achieved through a frequency stabilized reactance modulator.
• The stability of the whole circuit depends on the stability of the discriminator
• As the discriminator is turned to a frequency that is one-twentieth of the drift in the master oscillator frequency. The frequency drift is reduced to a great extent.

3. FM is a part of general class of modulation known as ______

1. Angle modulation
2. Phase modulation
3. Amplitude modulation
4. Frequency modulation

Explanation

Angle modulation is a class of carrier modulation that is used in telecommunications transmission systems.

The class comprises frequency modulation (FM) and phase modulation (PM) and is based on altering the frequency or the phase, respectively, of a carrier signal to encode the message signal.

Angle modulation varies a sinusoidal carrier signal in such a way that the angle of the carrier is varied according to the amplitude of the modulating baseband signal.

4. Foster Seeley discriminator uses a

1. Single tuned circuit
2. Double tuned circuit with primary and secondary tuned to the different frequency
3. Double tuned circuit with primary and secondary tuned to the same frequency
4. None of these

Answer.3. Double tuned circuit with primary and secondary tuned to the same frequency

Explanation

Foster Seeley discriminator is used in the demodulation of FM signal and it uses a double-tuned circuit with primary and secondary tuned to the same frequency.

• Discriminator circuits can generate electrical output directly proportional to the frequency deviation from the unmodulated RF carrier frequency.
• The simplest circuit could be a balanced slope detector.
• Foster Seeley makes use of two resonant circuits i.e Double tuned circuit one off-tuned to one side of unmodulated RF carrier frequency and the other off-tuned to the other side of it.

5. A 20 MHz carrier is modulated by a sinusoid of 1 kHz to produce a peak frequency deviation of 100 kHz. What is the approximate bandwidth? If the modulating signal is changed to 800 kHz, what is the bandwidth?

1. 2 kHz, 1600 kHz
2. 202 kHz, 1600 kHz
3. 202 kHz, 1800 kHz
4. 2 kHz, 1800 kHz

Explanation

According to Carson rule, BW is given as:

B.W = (β + 1) 2fm

B.W. = 2[Δf + fm]

B.W. = 2[Δf + fm]

For β < 1 (NBFM) case, only the adjacent two sidebands are significant and the bandwidth is similar to an AM case, i.e.

BW = 2 × fm

Given:

fc = 20 MHz,

fm = 1 kHz,

Δf = 100 kHz

β = 100k/1k = 100 > 1

So, from Carson rule:

BW = 2(Δf + fm)

BW = 2(100 + 1) = 202 kHz

Now, fm changes to 800 kHz

β = 100k/800k = 0.12 < 1. This is an NBFM signal.

BW = 2 fm = 2 × 800 k = 1600 kHz.

6. FM is called constant envelope because ______ of carrier wave is kept constant.

1. Frequency
2. Amplitude
3. Phase
4. Angle

Explanation

The constant envelope is achieved when a sinusoidal waveform reaches equilibrium in a specific system. In frequency modulation, the carrier amplitude remains constant, but its frequency is changed in accordance with the modulating signal. Specifically, the higher the amplitude of the information signal, the greater the frequency change.

7. Frequency curve is _______

1. Asymptotic to y-axis
2. Non-asymptotic to x-axis
3. Asymptotic to x-axis
4. None of these

Explanation

• Frequency curve is a graph of frequency distribution where the line is smooth.
• It is just like a frequency polygon.
• In the polygon is line is straight, but in the curve the line is smooth.
• It is an area diagram.
• It is the graphical representation of frequency distribution.
• The X-axis is marked with class intervals.
• The frequency curve is Asymptotic to the x-axis. Asymptotic to the x-axis” means that a function or curve is approaching the x-axis but never crosses it.
• The Y-axis is marked with frequencies.
• The beginning and end of the curve should touch the last class interval at the mad posts of the first and last interval.
• The area of the curve is equal to that of a histogram.

8. To produce frequency modulation using a phase modulator

1. The message signal must be integrated and then used for modulation.
2. The message signal must be differentiated and then used for modulation.
3. The phase-modulated signal must be integrated
4. The phase-modulated signal must be differentiated

Answer.1. The message signal must be integrated and then used for modulation.

Explanation

A standard frequency-modulated wave is written in the form:

${S_{FM}}\left( t \right) = A\:cos\left( {2\pi {f_c}t + 2\pi {k_f}\mathop \smallint \limits_0^t m\left( t \right).dt} \right)$

A standard phase-modulated wave is written in the form:

SPm(t) = AcCos[ωct + (Kp, m(t))]

m(t) = the modulating signal

ωc = Carrier frequency

Suppose, x(t) = $\mathop \smallint \limits_0^t m\left( t \right).dt$

When x(t) is applied at the phase modulator we will get the following signal at the output:

$S\left( t \right) = A\:cos\left( {2\pi {f_c}t + {k_p}x(t)} \right)$

putting the value of x(t), we get

$S\left( t \right) = A\:cos\left( {2\pi {f_c}t + {k_p}(\mathop \smallint \limits_0^t m\left( t \right).dt)} \right)$

This signal represents a standard FM signal with

2πkf = kp

9. Which of the following are the two most important classes of angle modulation?

1. Amplitude modulation, frequency modulation
2. Amplitude modulation, phase modulation
3. Frequency modulation, phase modulation
4. Single sideband amplitude modulation, phase modulation

Explanation

Angle modulation is a class of carrier modulation that is used in telecommunications transmission systems. The class comprises frequency modulation (FM) and phase modulation (PM) and is based on altering the frequency or the phase, respectively, of a carrier signal to encode the message signal. Angle modulation varies a sinusoidal carrier signal in such a way that the angle of the carrier is varied according to the amplitude of the modulating baseband signal.

10. Which is true in a frequency modulated system?

1. Variation of carrier amplitude does not affect the quality of reception
2. The amplitude of carrier is varied according to modulating signal
3. The transmission does not require line of sight between transmitter and receiver

Answer.1. Variation of carrier amplitude does not affect the quality of reception

Explanation

• Frequency Modulation is a modulation in which the frequency of the carrier wave is altered according to the instantaneous amplitude of the modulating signal, keeping phase and amplitude constant.
• So, the variation in carrier amplitude and carrier phase does not affect the signal in the receiving end.
• Line of sight (LoS) is a type of propagation that can transmit and receive data only where transmit and receive stations are in view of each other without any sort of an obstacle between them. Eg: FM radio, microwave, and satellite transmission.
• Frequency Modulation works on the Line of sight propagation.

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text:
# An improved quantum-inspired algorithm for linear regression

András Gilyén1, Zhao Song2, and Ewin Tang3

1Alfréd Rényi Institute of Mathematics
3University of Washington

### Abstract

We give a classical algorithm for linear regression analogous to the quantum matrix inversion algorithm [Harrow, Hassidim, and Lloyd, Physical Review Letters'09] for low-rank matrices [Wossnig, Zhao, and Prakash, Physical Review Letters'18], when the input matrix $A$ is stored in a data structure applicable for QRAM-based state preparation.

Namely, suppose we are given an $A \in \mathbb{C}^{m\times n}$ with minimum non-zero singular value $\sigma$ which supports certain efficient $\ell_2$-norm importance sampling queries, along with a $b \in \mathbb{C}^m$. Then, for some $x \in \mathbb{C}^n$ satisfying $\|x – A^+b\| \leq \varepsilon\|A^+b\|$, we can output a measurement of $|x\rangle$ in the computational basis and output an entry of $x$ with classical algorithms that run in $\tilde{\mathcal{O}}\big(\frac{\|A\|_{\mathrm{F}}^6\|A\|^6}{\sigma^{12}\varepsilon^4}\big)$ and $\tilde{\mathcal{O}}\big(\frac{\|A\|_{\mathrm{F}}^6\|A\|^2}{\sigma^8\varepsilon^4}\big)$ time, respectively. This improves on previous "quantum-inspired" algorithms in this line of research by at least a factor of $\frac{\|A\|^{16}}{\sigma^{16}\varepsilon^2}$ [Chia, Gilyén, Li, Lin, Tang, and Wang, STOC'20]. As a consequence, we show that quantum computers can achieve at most a factor-of-12 speedup for linear regression in this QRAM data structure setting and related settings. Our work applies techniques from sketching algorithms and optimization to the quantum-inspired literature. Unlike earlier works, this is a promising avenue that could lead to feasible implementations of classical regression in a quantum-inspired settings, for comparison against future quantum computers.

In this work, we combine two powerful ideas: stochastic gradient descent and the "quantum-inspired" access model of vectors and matrices. Algorithms in this access model have been previously used to demonstrate that certain quantum machine learning algorithms cannot give exponential speedups, and faster algorithms in this model imply stronger barriers to quantum speedup. So, to analyze the potential for quantum speedup in machine learning, we study the problem of linear regression, or solving a linear system $Ax=b$. We notice that, in the quantum-inspired setting, the quantum-like operations we can perform enable us to efficiently sample gradients of $f(x) = \tfrac12\|Ax-b\|^2$ when the matrix $A$ is low rank. This fits nicely with stochastic gradient descent techniques, so we use them to develop much faster algorithms over prior work, which was bottlenecked by its use of costly singular value decompositions. We break through this barrier and obtain a quartic dependence on precision, making significant progress towards practically applicable quantum-inspired algorithms. Later, Shao and Montanaro showed that in certain cases, variants of stochastic gradient descent can run even faster, with quadratic dependence on precision.

### ► References

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[6] András Gilyén, Yuan Su, Guang Hao Low, and Nathan Wiebe. Quantum singular value transformation and beyond: Exponential improvements for quantum matrix arithmetics''. In Proceedings of the 51st ACM Symposium on the Theory of Computing (STOC). Pages 193–204. (2019). arXiv:1806.01838.
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[9] Nai-Hui Chia, András Gilyén, Tongyang Li, Han-Hsuan Lin, Ewin Tang, and Chunhao Wang. Sampling-based sublinear low-rank matrix arithmetic framework for dequantizing quantum machine learning''. In Proceedings of the 52nd ACM Symposium on the Theory of Computing (STOC). Page 387–400. (2020). arXiv:1910.06151.
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[15] Leonard Wossnig, Zhikuan Zhao, and Anupam Prakash. Quantum linear system algorithm for dense matrices''. Physical Review Letters 120, 050502 (2018). arXiv:1704.06174.
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[16] Patrick Rebentrost, Masoud Mohseni, and Seth Lloyd. Quantum support vector machine for big data classification''. Physical Review Letters 113, 130503 (2014). arXiv:1307.0471.
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[17] Shantanav Chakraborty, András Gilyén, and Stacey Jeffery. The power of block-encoded matrix powers: Improved regression techniques via faster Hamiltonian simulation''. In Proceedings of the 46th International Colloquium on Automata, Languages, and Programming (ICALP). Pages 33:1–33:14. (2019). arXiv:1804.01973.
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arXiv:1804.01973

[18] Nai-Hui Chia, András Gilyén, Han-Hsuan Lin, Seth Lloyd, Ewin Tang, and Chunhao Wang. Quantum-inspired algorithms for solving low-rank linear equation systems with logarithmic dependence on the dimension''. In Proceedings of the 31st International Symposium on Algorithms and Computation (ISAAC). Pages 47:1–47:17. (2020). arXiv:1811.04852 and 1811.04909 (merged).
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[22] Srinivasan Arunachalam, Vlad Gheorghiu, Tomas Jochym-O'Connor, Michele Mosca, and Priyaa Varshinee Srinivasan. On the robustness of bucket brigade quantum RAM''. New Journal of Physics 17, 123010 (2015). arXiv:1502.03450.
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[28] András Gilyén, Seth Lloyd, and Ewin Tang. Quantum-inspired low-rank stochastic regression with logarithmic dependence on the dimension'' (2018). arXiv:1811.04909.
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[29] Nai-Hui Chia, Han-Hsuan Lin, and Chunhao Wang. Quantum-inspired sublinear classical algorithms for solving low-rank linear systems'' (2018). arXiv:1811.04852.
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[30] David P. Woodruff. Sketching as a tool for numerical linear algebra''. Foundations and Trends in Theoretical Computer Science 10, 1–157 (2014).
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[32] Changpeng Shao and Ashley Montanaro. Faster quantum-inspired algorithms for solving linear systems'' (2021). arXiv:2103.10309.
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[35] Petros Drineas, Ravi Kannan, and Michael W Mahoney. Fast Monte Carlo algorithms for matrices II: Computing a low-rank approximation to a matrix''. SIAM Journal on Computing 36, 158–183 (2006).
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### Cited by

[1] Quynh T. Nguyen, Bobak T. Kiani, and Seth Lloyd, "Quantum algorithm for dense and full-rank kernels using hierarchical matrices", arXiv:2201.11329.

[2] Benjamin A. Cordier, Nicolas P. D. Sawaya, Gian G. Guerreschi, and Shannon K. McWeeney, "Biology and medicine in the landscape of quantum advantages", arXiv:2112.00760.

[3] Adam Bouland, Wim van Dam, Hamed Joorati, Iordanis Kerenidis, and Anupam Prakash, "Prospects and challenges of quantum finance", arXiv:2011.06492.

[4] Amirhossein Nourbakhsh, Mark Nicholas Jones, Kaur Kristjuhan, Deborah Carberry, Jay Karon, Christian Beenfeldt, Kyarash Shahriari, Martin P. Andersson, Mojgan A. Jadidi, and Seyed Soheil Mansouri, "Quantum Computing: Fundamentals, Trends and Perspectives for Chemical and Biochemical Engineers", arXiv:2201.02823.

[5] Xiao-Ming Zhang, Tongyang Li, and Xiao Yuan, "Quantum State Preparation with Optimal Circuit Depth: Implementations and Applications", arXiv:2201.11495.

[6] Shantanav Chakraborty, Aditya Morolia, and Anurudh Peduri, "Quantum Regularized Least Squares", arXiv:2206.13143.

[7] Bujiao Wu, Maharshi Ray, Liming Zhao, Xiaoming Sun, and Patrick Rebentrost, "Quantum-classical algorithms for skewed linear systems with an optimized Hadamard test", Physical Review A 103 4, 042422 (2021).

[8] Patrick Rall, "Faster Coherent Quantum Algorithms for Phase, Energy, and Amplitude Estimation", arXiv:2103.09717.

[9] Changpeng Shao and Ashley Montanaro, "Faster quantum-inspired algorithms for solving linear systems", arXiv:2103.10309.

[10] Iordanis Kerenidis and Anupam Prakash, "Quantum machine learning with subspace states", arXiv:2202.00054.

[11] Sevag Gharibian and François Le Gall, "Dequantizing the Quantum Singular Value Transformation: Hardness and Applications to Quantum Chemistry and the Quantum PCP Conjecture", arXiv:2111.09079.

[12] Chenyi Zhang, Jiaqi Leng, and Tongyang Li, "Quantum algorithms for escaping from saddle points", arXiv:2007.10253.

[13] Daniel Chen, Yekun Xu, Betis Baheri, Samuel A. Stein, Chuan Bi, Ying Mao, Qiang Quan, and Shuai Xu, "Quantum-Inspired Classical Algorithm for Slow Feature Analysis", arXiv:2012.00824.

[14] Kazuya Kaneko, Koichi Miyamoto, Naoyuki Takeda, and Kazuyoshi Yoshino, "Linear regression by quantum amplitude estimation and its extension to convex optimization", Physical Review A 104 2, 022430 (2021).

[15] Franco D. Albareti, Thomas Ankenbrand, Denis Bieri, Esther Hänggi, Damian Lötscher, Stefan Stettler, and Marcel Schöngens, "A Structured Survey of Quantum Computing for the Financial Industry", arXiv:2204.10026.

[16] Ebrahim Ardeshir-Larijani, "Parametrized Complexity of Quantum Inspired Algorithms", arXiv:2112.11686.

The above citations are from SAO/NASA ADS (last updated successfully 2022-08-13 16:16:55). The list may be incomplete as not all publishers provide suitable and complete citation data.

On Crossref's cited-by service no data on citing works was found (last attempt 2022-08-13 16:16:54).


text:
Conference paper Open Access

Understanding the challenges behind Electric Vehicle usage by drivers - a case study in the Madeira Autonomous Region

Luísa Barros; Mary Barreto; Lucas Pereira

Citation Style Language JSON Export

{
"DOI": "10.1145/3401335.3401667",
"author": [
{
"family": "Lu\u00edsa Barros"
},
{
"family": "Mary Barreto"
},
{
"family": "Lucas Pereira"
}
],
"issued": {
"date-parts": [
[
2020,
6,
1
]
]
},
"abstract": "
Electric Vehicles (EV) adoption targets have been set by governments from countries throughout Europe, related to the European goals, for the decarbonization of the road transport sector. The change for electric vehicle technology can be challenging to EV users for several reasons such as battery autonomy, time to charge the vehicle, and the different driving conditions. The work in this paper aims to study how users from Madeira and Porto Santo islands deal with the challenges of EV usage. Furthermore, this paper also studies the role of the orography in the Regenerative Braking System technology integrated into electric vehicles. To assess such information, an online questionnaire was prepared and sent out to the electric vehicle community of both islands. The main results of this study show drivers' preference to charge the vehicles at their household and that users are satisfied with the vehicle's technology. Also, users' battery range anxiety did not seem to have a significant impact. Moreover, from the drivers' point of view, there is still the need to study the role of orography, while using the regenerative braking system.
",
"title": "Understanding the challenges behind Electric Vehicle usage by drivers - a case study in the Madeira Autonomous Region",
"type": "paper-conference",
"id": "4004633"
}
74
147
views


text:
# UnitGaussianElimination¶

References: J-G. Dumas, F. Heckenbach, D. Sauders, V. Welker: Computing simplicial homology based on efficient Smith normal form algorithms. Descrition: Gaussion elimination using only 1 or -1 as pivots
pre_gauss(m) performs Gaussian eliminaton on rows of m using only 1 and -1 as pivots. Note: m is modified in place
pre_lr(m, pi, pj) is like pre_gauss, but records positions of pivots in pi and pj and returns transformation matrix. m, pi, pj are modified in place
pre_smith(m) first performs pre_gauss(m) and then drops all rows and colums of m contaning pivots.


text:
# z-scores or raw scores for continuous variables in a mixed-effects model

I am trying to use a mixed-effects model to examine the effects of three teaching approaches on the learning of English past tense measured through language tests at five testing points. The dependent variable of my model is the learners' test score. The fixed-effect variables are group (three treatment group and a control group) and testing time (five testing points including a pre-test and four post-tests). In addition, I also set subjects as the random-effect variable. Pre-test scores are controlled for as a covariate in the model because they are not comparable among the four groups.

My model is:

mod<-lmer(score~pre-test+group*time+(1+pre-test|subject),data=EI,REML=FALSE).

The full mark of the five tests is the same, which is 24. My questions are: Should I use the raw scores or z-scores for the covariate (pre-test) in this model? If yes, should I convert raw scores to z-scores for the dependent variable as well?

• Can you explain why the pre-test scores are not comparable among the groups? Are the scores at the other testing points likewise not comparable? – Darren James Sep 22 '17 at 15:07
• Hi Darren, thank you for your question. The four groups being compared cannot be assumed to be equivalent because there are significant between-group differences on pre-test. If the influence of pre-test scores is not eliminated in the model, it will be confound with the effects of the treatment. That is, learners with high pre-test scores are most likely to achieve high post-test scores in spite of the treatment, which thus causes difficulties in interpreting the significant group differences identified at the other four testing points. – Summer Fu Sep 22 '17 at 22:07
• Thanks for clarifying. Have you considered using gain scores? Doing so would be justified as long as the test scores are on the same scale. It would account for the between-group differences and also produce estimates that are easy to interpret. – Darren James Sep 25 '17 at 17:55