Rule Of Signs Research Articles

Limitations of Mean-Based Algorithms for Trace Reconstruction at Small Edit Distance

Trace reconstruction considers the task of recovering an unknown string <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathbf {x}\in \{0,1\}^{n}$ </tex-math></inline-formula> given a number of independent “traces”, i.e., subsequences of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathbf {x}$ </tex-math></inline-formula> obtained by randomly and independently deleting every symbol of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathbf {x}$ </tex-math></inline-formula> with some probability <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$p$ </tex-math></inline-formula> . The information-theoretic limit of the number of traces needed to recover a string of length <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula> is still unknown. This limit is essentially the same as the number of traces needed to determine, given strings <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathbf {x}$ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathbf {y}$ </tex-math></inline-formula> and traces of one of them, which string is the source. The most-studied class of algorithms for the worst-case version of the problem are “mean-based” algorithms. These are a restricted class of distinguishers that only use the mean value of each coordinate on the given samples. In this work we study limitations of mean-based algorithms on strings at small Hamming or edit distance. We show that, on the one hand, distinguishing strings that are nearby in Hamming distance is “easy” for such distinguishers. On the other hand, we show that distinguishing strings that are nearby in edit distance is “hard” for mean-based algorithms. Along the way, we also describe a connection to the famous Prouhet-Tarry-Escott (PTE) problem, which shows a barrier to finding explicit hard-to-distinguish strings: namely such strings would imply explicit short solutions to the PTE problem, a well-known difficult problem in number theory. Furthermore, we show that the converse is also true, thus, finding explicit solutions to the PTE problem is equivalent to the problem of finding explicit strings that are hard-to-distinguish by mean-based algorithms. Our techniques rely on complex analysis arguments that involve careful trigonometric estimates, and algebraic techniques that include applications of Descartes’ rule of signs for polynomials over the reals.

Application of Addition sign rules in preparing general multi-column worksheet

Application of Addition sign rules in preparing general multi-column worksheet

On generalizing Descartes' rule of signs to hypersurfaces

We give partial generalizations of the classical Descartes' rule of signs to multivariate polynomials (with real exponents), in the sense that we provide upper bounds on the number of connected components of the complement of a hypersurface in the positive orthant. In particular, we give conditions based on the geometrical configuration of the exponents and the sign of the coefficients that guarantee that the number of connected components where the polynomial attains a negative value is at most one or two. Our results fully cover the cases where such an upper bound provided by the univariate Descartes' rule of signs is one. This approach opens a new route to generalize Descartes' rule of signs to the multivariate case, differing from previous works that aim at counting the number of positive solutions of a system of multivariate polynomial equations.

Integrating Secure Communications Into Frequency Hopping MIMO Radar With Improved Data Rate

Dual-function radar-communication (DFRC) based on frequency hopping (FH) MIMO radar (FH-MIMO DFRC) achieves symbol rate much higher than radar pulse repetition frequency. Such DFRC, however, is prone to eavesdropping due to the spatially uniform illumination of an FH-MIMO radar. In this paper, we reveal the potential of using permutations of hopping frequencies to achieve secure and high-speed FH-MIMO DFRC. Specifically, we identify the angle-dependent issue in detecting permutations and develop an element-wise phase compensation (EPC) to solve the issue for a legitimate user (Bob). EPC makes the demodulation at an eavesdropper (Eve) conditioned on knowing the angle-of-departure (AoD) of Bob. We also propose the random sign reversal (RSR) technique which randomly selects several antennas over hops and reverses their signs. Owing to EPC, there is a sign rule available for Bob. We employ the rule and develop a low-complexity algorithm for Bob to remove RSR. We further prove that, given the same signal-to-noise ratio, RSR plus EPC make the demodulation performance of Eve inferior to that of Bob in most angular regions. Confirmed by simulation, our design achieves substantially high physical layer security for FH-MIMO DFRC, improves demodulation performance compared with existing designs, and reduces mutual interference among radar targets.

Penerapan Model Discovery Learning untuk Meningkatan Kemampuan Berpikir Kritis Siswa

The high number of traffic accidents on the highway, precisely in the city of Medan, is a factor in the death of children aged 14-23 years. One of them is the lack of attention and education of parents about traffic sign. In this board game design, the aim is to learn the rules of traffic signs for children aged 7-11 years. In the design of this game, there is a board game that contains various information about traffic sign and road markings. This game will produce games that are no less exciting and add a lot if insight to children and teenagers who want to know the rules of traffic signs in it.

Penerapan Model Discovery Learning untuk Meningkatan Kemampuan Berpikir Kritis Siswa

The high number of traffic accidents on the highway, precisely in the city of Medan, is a factor in the death of children aged 14-23 years. One of them is the lack of attention and education of parents about traffic sign. In this board game design, the aim is to learn the rules of traffic signs for children aged 7-11 years. In the design of this game, there is a board game that contains various information about traffic sign and road markings. This game will produce games that are no less exciting and add a lot if insight to children and teenagers who want to know the rules of traffic signs in it.

An efficient nonstandard computer method to solve a compartmental epidemiological model for COVID-19 with vaccination and population migration

Background and objective: In this manuscript, we consider a compartmental model to describe the dynamics of propagation of an infectious disease in a human population. The population considers the presence of susceptible, exposed, asymptomatic and symptomatic infected, quarantined, recovered and vaccinated individuals. In turn, the mathematical model considers various mechanisms of interaction between the sub-populations in addition to population migration. Methods: The steady-state solutions for the disease-free and endemic scenarios are calculated, and the local stability of the equilibium solutions is determined using linear analysis, Descartes’ rule of signs and the Routh–Hurwitz criterion. We demonstrate rigorously the existence and uniqueness of non-negative solutions for the mathematical model, and we prove that the system has no periodic solutions using Dulac’s criterion. To solve this system, a nonstandard finite-difference method is proposed. Results: As the main results, we show that the computer method presented in this work is uniquely solvable, and that it preserves the non-negativity of initial approximations. Moreover, the steady-state solutions of the continuous model are also constant solutions of the numerical scheme, and the stability properties of those solutions are likewise preserved in the discrete scenario. Furthermore, we establish the consistency of the scheme and, using a discrete form of Gronwall’s inequality, we prove theoretically the stability and the convergence properties of the scheme. For convenience, a Matlab program of our method is provided in the appendix. Conclusions: The computer method presented in this work is a nonstandard scheme with multiple dynamical and numerical properties. Most of those properties are thoroughly confirmed using computer simulations. Its easy implementation make this numerical approach a useful tool in the investigation on the propagation of infectious diseases. From the theoretical point of view, the present work is one of the few papers in which a nonstandard scheme is fully and rigorously analyzed not only for the dynamical properties, but also for consistently, stability and convergence.

Canonical vertex formalism in DT theory of toric Calabi-Yau 4-folds

Motivated by previous computations of Y. Cao, M. Kool and the author, we propose square roots and sign rules for the vertex and edge terms that compute Donaldson-Thomas invariants of a toric Calabi-Yau 4-fold, and prove that they are canonical, exploiting the combinatorics of plane and solid partitions.

The Influence of Parenting Styles Types on the Intelligence and Decision Making of the Deaf

Abstract This study aimed to investigate the effect of types of parenting styles on intelligence and decision-making among the deaf. The tools comprised the Wechsler Intelligence Scale-4th edition (WISC-4) for deaf, using sign language, was used to assess deaf students’ intelligence and a scale of professional decision-making. The sample of the study included 157 deaf students in deaf schools in Jordan whose ages ranged from 13 to 16.11 years. WISC-4 was administered using sign language. The results showed that the democratic pattern was high, the level of intelligence for deaf students was average, and the professional decision-making was of a medium level. Also, there was a negative relationship between the authoritarian style, the permissive pattern, and the overall intelligence. There were statistically significant differences in the permissive type and the intelligence of the deaf due to gender in favor of females. Significant differences in speech comprehension, working memory, and overall intelligence were found in favor of mild hearing impairment. There were significant differences in the IQ level of the age variable in favor of students aged 13 years. The study recommends more research regarding the effect of hearing impairment on the psychological aspects of professional decision-making and providing hearing parents with training in sign language and rules for communicating with their deaf children. Keywords: Sign language, Deaf, The family, Family upbringing, Wechsler Scale-4, Intelligence.

Hyperbolic polynomials and rigid orders of moduli

A hyperbolic polynomial (HP) is a real univariate polynomial with all roots real. By Descartes' rule of signs a HP with all coefficients nonvanishing has exactly $c$ positive and exactly $p$ negative roots counted with multiplicity, where $c$ and $p$ are the numbers of sign changes and sign preservations in the sequence of its coefficients. We consider HPs with distinct moduli of the roots. We ask the question when the order of the moduli of the negative roots w.r.t. the positive roots on the real positive half-line completely determines the signs of the coefficients of the polynomial. When there is at least one positive and at least one negative root this is possible exactly when the moduli of the negative roots interlace with the positive roots (hence half or about half of the roots are positive). In this case the signs of the coefficients of the HP are either $(+,+,-,-,+,+,-,-,\ldots )$ or $(+,-,-,+,+,-,-,+,\ldots )$.

Stability and Hopf bifurcation analysis of a delayed eco-epidemiological model of IYSV disease dynamics in onion plants with nonlinear saturated incidence and logistic growth

Iris Yellow Spot Disease (IYSD), caused by Iris Yellow Spot Virus (IYSV) is a destructive and fastspreading virus disease of onion plants worldwide. It is mainly transmitted by an insect vector called thrips tabaci in a persistent and propagative manner and as such, there is a significant latent time after acquisition of the virus by the vector and an incubation time is needed for the appearance of disease symptoms on plants. In this paper, we formulate and analyze a non-linear mathematical model to explore the dynamics of IYSV disease in onion plants using system of delay differential equations by incorporating incubation and latent periods as time delays factors. The delays are introduced by adding an exposed population for onion plants representing the plants that are infected but not yet infective and by taking into account that there is fraction of the newly exposed onion plants that do not die during incubation period before becoming infective. It is assumed that the onion plant grows logistically in the farm so that the total onion plant population is taken as variable. The local stability of the disease-free equilibrium in the presence of delays is investigated using Descartes’s rule of signs. We establish the sufficient conditions for the stability of the endemic equilibrium in presence of delays and we investigate the occurrence of Hopf bifurcation when certain conditions are satisfied by considering the two delays as bifurcation parameters. We compute the critical values of the delays which preserve the local asymptotic stability of the endemic equilibrium and the model shows an oscillatory behavior beyond these critical values. Finally, numerical simulations are performed and displayed graphically to support the analytical results, and the eco-epidemiological implications of the key outcomes are briefly discussed.

Helicity observations of active regions during the exchange period of Solar Cycle 24 and 25

ABSTRACT Using vector magnetic field data from the Helioseismic and Magnetic Imager instrument onboard the Solar Dynamics Observatory, we study the signs of helicity (magnetic twist αav, z-component of current helicity Hc) and tilt angle of 85 sample active regions (ARs) that appeared on the central solar disc (within ±45° from disc centre) between December 2018 and November 2020. This time range spans the exchange period of Solar Cycle 24 and 25. The main findings are as follows: (1) As a whole, 62 per cent of sample ARs follow the helicity hemispherical sign rule, and our observational results do not show any hemispherical rule sign reversal at the end or beginning of a Solar Cycle. (2) Interestingly, there is no significant statistical relationship between helicity and tilt angle, as in contrast with the general idea on the conservation of magnetic helicity in the solar convection zone inferred by the relationship between the photospheric helicity and tilt angle. It is also found that the hemispherical tendency of helicity and tilt angle is more obvious for ARs at high latitudes, and the hemispherical preference is more obvious for ARs with magnetic twist and writhe of the opposite signs than for ARs with the same signs.

Entanglement in bipartite quantum systems: Euclidean volume ratios and detectability by Bell inequalities

Euclidean volume ratios between quantum states with positive partial transpose and all quantum states in bipartite systems are investigated. These ratios allow a quantitative exploration of the typicality of entanglement and of its detectability by Bell inequalities. For this purpose a new numerical approach is developed. It is based on the Peres–Horodecki criterion, on a characterization of the convex set of quantum states by inequalities resulting from Newton identities and from Descartes’ rule of signs, and on a numerical approach involving the multiphase Monte Carlo method and the hit-and-run algorithm. This approach confirms not only recent analytical and numerical results on two-qubit, qubit-qutrit, and qubit-four-level qudit states but also allows for a numerically reliable numerical treatment of so far unexplored qutrit–qutrit states. Based on this numerical approach with the help of the Clauser–Horne–Shimony–Holt inequality and the Collins–Gisin inequality the degree of detectability of entanglement is investigated for two-qubit quantum states. It is investigated quantitatively to which extent a combined test of both Bell inequalities can increase the detectability of entanglement beyond what is achievable by each of these inequalities separately.

Piezoelectricity in binary wurtzite semiconductors: a first-principles study

Using first-principles calculations, we investigate piezoelectricity in a wide range of binary wurtzite semiconductors. We find that piezoelectricity is intimately related to the bond character, e.g. the negative longitudinal piezoelectric effect (NLPE) tends to occur in covalent compounds. We further find a universal sign rule (negative clamped-ion term and positive internal-strain term) for piezoelectricity, and the NLPE occurs as a result of the domination of the former over the latter. Moreover, there exists an inverse linear correlation between the longitudinal and transverse piezoelectric coefficients. This work may offer a simple criterion for efficient computational screening of materials exhibiting the NLPE.

Superradiant stability of five and six-dimensional extremal Reissner\u2013Nordstrom black holes

We revisit the superradiant stability of five and six-dimensional extremal Reissner–Nordstrom black holes under charged massive scalar perturbation with a new analytical method. In each case, it is analytically proved that the effective potential experienced by the scalar perturbation has only one maximum outside the black hole horizon and no potential well exists for the superradiance modes. So the five and six-dimensional extremal Reissner–Nordstrom black holes are superradiantly stable. The new method we developed is based on the Descartes’ rule of signs for the polynomial equations. Our result provides a complementary support of previous studies on the stability of higher dimensional extremal Reissner–Nordstrom black holes based on numerical methods.

Optimal Descartes’ rule of signs for systems supported on circuits

Optimal Descartes’ rule of signs for systems supported on circuits

On the Roots of the Modified Orbit Polynomial of a Graph

The definition of orbit polynomial is based on the size of orbits of a graph which is OG(x)=∑ix|Oi|, where O1,…,Ok are all orbits of graph G. It is a well-known fact that according to Descartes’ rule of signs, the new polynomial 1−OG(x) has a positive root in (0,1), which is unique and it is a relevant measure of the symmetry of a graph. In the current work, several bounds for the unique and positive zero of modified orbit polynomial 1−OG(x) are investigated. Besides, the relation between the unique positive root of OG in terms of the structure of G is presented.

A systematic search for switch-like behavior in type II toxin-antitoxin systems.

Bistable switch-like behavior is a ubiquitous feature of gene regulatory networks with decision-making capabilities. Type II toxin-antitoxin (TA) systems are hypothesized to facilitate a bistable switch in toxin concentration that influences the dormancy transition in persister cells. However, a series of recent retractions has raised fundamental questions concerning the exact mechanism of toxin propagation in persister cells and the relationship between type II TA systems and cellular dormancy. Through a careful modeling search, we identify how sp: bistablilty can emerge in type II TA systems by systematically modifying a basic model for the RelBE system with other common biological mechanisms. Our systematic search uncovers a new combination of mechanisms influencing bistability in type II TA systems and explores how toxin bistability emerges through synergistic interactions between paired type II TA systems. Our analysis also illustrates how Descartes' rule of signs and the resultant can be used as a powerful delineator of bistability in mathematical systems regardless of application.

Mathematical model of schistosomiasis with health education and molluscicide intervention

In this article, a mathematical model is developed to study the impact of health education and molluscicide intervention on the spread of schistosomiasis. The model constructed consists of seven ordinary differential equations that describe susceptible human, latent human, infectious human, susceptible snail, infected snail, miracidia and cercarie. After analyzing non-negativity and boundedness of solutions of the model, we determine the disease free equilibrium point and the endemic equilibrium point as well as their existence conditions. The basic reproduction number is determined using the next generation matrix approach. The local stability condition of the disease-free equilibrium point is proved by using linearization and Descartes’ sign rule.. The Center Manifold Theory is used to prove the local stability condition of the endemic equilibrium point and to identify the existence of bifurcation. We constructed Lyapunov function to show that the disease-free equilibrium point is globally asymptotically stable under sufficient condition. We present numerical simulations to support our theoretical study. Numerical simulations show that health education and molluscicide intervention are able to reduce schistosomiasis cases in human and snail populations. Molluscicide intervention is a very effective method to control the spread of schistosomiasis.

Hermeneutics of Measurement

The topic of our study is the structure of temporality for different human acts and its consequences for a theory of measurement. We begin by studying a specific group of acts that we denote “complementary asymmetric acts”. To do this, we will introduce a paradigmatic example, the complementary acts of writing and reading. The act of writing is, from the point of view of time passing, directed towards the future, because it is intended to be read when the written text is finalized. In contrast, the act of reading is directed towards the past, for it will transpire after the act of writing. Thus, the asymmetric acts of writing and reading occur in an inverse order in respect to the flow of time. Acts that are polarized to the present will be denoted as parallel acts. They differ from complementary acts by not sharing the same referent object. Each parallel act presents their own object. For instance, [John brings Mary a bouquet of flowers] and [Mary is grateful and sends a book to John] are two parallel acts. We observe that the first act is polarized towards the future, while the second act is polarized towards the past. However, these polarizations approach to the present by excess or by default. We observe that while the act of measurement is a parallel act, the experimental act is a complementary act. We noticed that in a chain of acts, the rules of polarization follow the rules of signs of algebra. For instance, in the case of complementary acts we found that the signs follow the rules of multiplication and in the case of parallel acts follow the rules of the signs of the sum. The polarization of acting can explain some of the perplexities of measuremnt of quantum phenomena.