Congruence Problem Research Articles

Simon's congruence pattern matching

The Simon's congruence problem is to determine whether or not two strings have the same set of subsequences of length no greater than a given integer, and the problem can be answered in linear time. We consider the Simon's congruence pattern matching problem that looks for all substrings of a text that are congruent to a pattern under the Simon's congruence. We propose a linear time algorithm by reusing results from previous computations with the help of new data structures called X-trees and Y-trees. Moreover, we investigate several variants of the problem such as identifying the shortest substring or subsequence of the text that is congruent to the pattern under the Simon's congruence, or finding frequent matchings. We design efficient algorithms for these problems. We conclude the paper with two open problems: finding the longest congruent subsequence and optimizing the pattern matching problem.

Congruence of rational matrices defined by an integer matrix

We study algorithms that construct an invertible matrix B∈Mn(Z) that defines congruence Btr·X·B=Y of given square rational matrices X,Y∈Mn(Q). We describe a general algorithm and discuss special cases of positive-definite and singular matrices. In the first case, the algorithm solves the decision problem and unequivocally determines if such an integer matrix exists.Since the problem of isomorphism of various finite structures can be viewed as a special case of matrix congruence problem, our results are applicable in this setting. We discuss this topic and show that the presented algorithms solve this problem in the case of partially ordered sets, vertex and edge labeled directed and undirected graphs. Moreover, they allow computing the automorphism group Aut(G) of a given (di)graph G.The results of this work are applicable in the general framework of Coxeter spectral analysis of signed graphs Δ introduced in (SIAM J. Discrete Math. 27:827–854, 2013) as they make it possible to calculate strong and weak Gram Z-congruences. Moreover, they can be used to compute isotropy groups and thus are useful in the study of matrix morsifications in the sense of (J. Pure Appl. Algebra 215:3–34, 2011).

Cut and paste invariants of manifolds via algebraic K-theory

Recent work of Inna Zakharevich and Jonathan Campbell has focused on building machinery for studying scissors congruence problems via algebraic K-theory, and applying these tools to studying the Grothendieck ring of varieties. In this paper we give a new application of their framework: we construct a K-theory space that recovers the classical SK (“schneiden und kleben,” German for “cut and paste”) groups for manifolds on π0, and we construct a derived version of the Euler characteristic.

Диалектика творения и проективная структура пространства

The article considers creationism as a historically relevant principle in the scientific and philosophic aspects denoting the ontological structure of the world. Outside of the religious interpretation, the author speaks of the dialectics of creation, which is revealed as an implicative connection of the one and nothing. Logical inversion (logical turn), acting from within this implicative connection, is postulated as the principle of a fundamental negation, which, according to the author, forms the true and dramatic essence of the world as a creation. The author distances himself from the widespread discussion between evolutionism and scientific creationism, stating that it does not correspond to the very subject of creationism, understood as the implication of a real from nothing. The author focuses on considering ‘nothing’ as a purely dialectical / metaphysical principle and relies partly on the Hegel’s dialectic of ‘being’ and ‘nothing’, and partly on the neoplatonic concept of the one. Rejecting the medieval interpretation of the temporal beginning and the Hegel’s identity, he deduces a scheme of the logical connection between the one and the difference, which postulates the inversion (turnover) forming the creation - the one and the difference disjunctively change places, the one becomes the real, and the difference out of the one becomes nothing. It is argued that this postulate, in particular, refutes the thesis about the ‘fall into sin’. In the second part of the article, a spatial-phenomenological hypothesis is presented: the author provides a description of the space as a geometrical-semantic plane (projective structure). This hypothesis follows from the phenomenological problem of the duality of a geometric object, which results in the problem of ontological transition between a point and a line (in the aporia of the Eleats) and the related problem of spatial congruence / parallelism. According to the author, the potential for solving these not essentially mathematical, but metaphysical questions is the projective geometry, in which parallel lines intersect at ‘point at infinity’, and space is complemented by the ‘plane at infinity’. The essence of the solution consists, firstly, in the assumption of the single plane, which underlies the transition, and secondly, in the description of the perceived world as a result of a specific turn over and closure of this plane, forming the projective structure. The key in this part is the demonstration of the surface of a three-dimensional object as a phenomenon of perceptual-semantic unfolding, which can be imagined as an action of consciousness, consistently reducing the usual scheme. An important aspect of considering the projective structure is the correlation with ‘the Plane’ by G. Deleuze. The general idea of the article is that the dialectical scheme of creation and the projective structure of the space coincide: the logical inversion (logical turn), acting in connection of the one and nothing, and projective structural turnover – are the same things.

Party-voter congruence in Turkish politics: the ivory tower argument tested

ABSTRACT ‘Ivory tower’ is frequently used phrase when Turkish executive politicians question the representativeness of other parties or their members. The intention of this claim is to provoke other parties into a discussion about the legitimacy of the targeted party. This research aims to shed a light on the problem of party-voter congruence in Turkish politics, which has important implications for the representativeness of Turkish political parties. Comparing the three major political parties in Turkey; the current study investigates to what extent these political parties’ manifesto documents, fail to connect with their constituencies’ policy positions on four prominent issues in Turkish politics: Left-right political positioning, democratic support, support for the military, and support for a controlled economy. Party level Manifesto Project data and aggregated individual level World Values Survey (WVS) data were combined for the analysis of this research and analysed by using a series of Ordinary Least Squares (OLS) regression analysis. The findings suggest that the ivory tower claim is largely correct for all three political parties investigated. Finally, these findings also have important implications for the legitimacy of the Turkish democratic political system.

Geometry of fanning curves in divisible Grassmannians

We study the geometry of fanning curves in the Grassmann manifold of n-dimensional subspaces of Rkn; we construct a complete system of invariants which solve the congruence problem. The geometry of the invariants themselves in terms of equivariant models of the relevant spaces of jets is studied; in particular we provide a geometrical characterization of the flat curves.

Limitation Period In Case-Law Of European Court Of Human Rights

Limitation period is the time for an aggrieved person to apply to court. Notwithstanding that aggrieved person after the limitation period has lapsed does not lose substantial right, such a person does lose a right to apply to court for protection. Thus in the situation when a limitation period has lapsed substantial and procedural rules are tightly intertwined. On the one hand, this situation is about some requirements for bringing an action to the court; on the other hand, the loss of judicial protection significantly decreases the value of the substantial right. That is why the improper application of limitation period potentially can threaten all fundamental human rights. Limitation period is a traditional issue in private law. That is why many scholars have addressed it. T. M. Vakhonyeva, V. V. Luts’, O. V. Pushnyak, V. I. Tsikalo, O. V. Shovkova are amongst them. Nevertheless the issue has never been analyzed systematically through the perspective of European Convention on Human Rights and Fundamental Freedoms.The main objective of the paper is to analyze the limitation period from the standpoint of its congruence to different provisions embodied in European Convention on Human Rights and Fundamental Freedoms.First of all the author pays attention to ECtHR case-law concerning the right to a fair trial. In that context limitation period is deemed to constitute a restriction of a right to a fair trial. But such a restriction is not in itself inconsistent with the Convention. In many cases such a restriction is justified first and foremost for the sake of providing legal certainty, which is one of the important aspects of rule of law. Also the author addresses the problem of congruence of limitation period to some other provisions of ECHR, such as: prohibition of discrimination, right to respect for private and family life, protection of property.Limitation period constitute a restriction of a right to access to court. Such a restriction is justified if (a) it does not restrict a right to access to court in such a way that the very essence of that right is nullified; (b) it has a legitimate purpose; (c) the proper balance between the purpose aimed and the restriction is struck. In order for the limitation period to be proportionate with the aim of providing legal certainty, the following requirements should be met: (i) the limitation period is not unduly short; (ii) the application of limitation period is foreseeable; (iii) the application of limitation period is flexible (i.e. it is capable of taking into account different individual characteristics of each case).Recent research and publications analysis. Limitation period is a traditional issue in private law. That is why many scholars have addressed it. T. M. Vakhonyeva, V. V. Luts', O. V. Pushnyak, V. I. Tsikalo, O. V. Shovkova are amongst them. Nevertheless the issue has never been analyzed systematically through the perspective of European Convention on Human Rights and Fundamental Freedoms.Paper objective. The main objective of the paper is to analyze the limitation period from the standpoint of its congruence to different provisions embodied in European Convention on Human Rights and Fundamental Freedoms.Paper main body. First of all the author pays attention to ECtHR case-law concerning the right to a fair trial. In that context limitation period is deemed to constitute a restriction of a right to a fair trial. But such a restriction is not in itself inconsistent with the Convention. In many cases such a restriction is justified first and foremost for the sake of providing legal certainty, which is one of the important aspects of rule of law. Also the author addresses the problem of congruence of limitation period to some other provisions of ECHR, such as: prohibition of discrimination, right to respect for private and family life, protection of property.Conclusions of the research. Limitation period constitute a restriction of a right to access to court. Such a restriction is justified if (a) it does not restrict a right to access to court in such a way that the very essence of that right is nullified; (b) it has a legitimate purpose; (c) the proper balance between the purpose aimed and the restriction is struck. In order for the limitation period to be proportionate with the aim of providing legal certainty, the following requirements should be met: (i) the limitation period is not unduly short; (ii) the application of limitation period is foreseeable; (iii) the application of limitation period is flexible (i.e. it is capable of taking into account different individual characteristics of each case).

Multiplex congruence network of natural numbers

Congruence theory has many applications in physical, social, biological and technological systems. Congruence arithmetic has been a fundamental tool for data security and computer algebra. However, much less attention was devoted to the topological features of congruence relations among natural numbers. Here, we explore the congruence relations in the setting of a multiplex network and unveil some unique and outstanding properties of the multiplex congruence network. Analytical results show that every layer therein is a sparse and heterogeneous subnetwork with a scale-free topology. Counterintuitively, every layer has an extremely strong controllability in spite of its scale-free structure that is usually difficult to control. Another amazing feature is that the controllability is robust against targeted attacks to critical nodes but vulnerable to random failures, which also differs from ordinary scale-free networks. The multi-chain structure with a small number of chain roots arising from each layer accounts for the strong controllability and the abnormal feature. The multiplex congruence network offers a graphical solution to the simultaneous congruences problem, which may have implication in cryptography based on simultaneous congruences. Our work also gains insight into the design of networks integrating advantages of both heterogeneous and homogeneous networks without inheriting their limitations.

Micro-phase measuring profilometry: Its sensitivity analysis and phase unwrapping

Global illumination affects shape measurement accuracy, and phase unwrapping is an important problem in phase measuring profilometry. In this paper, a micro-phase measuring profilometry is proposed to reduce the effects of global illumination. The wrapped phase error level of the proposed method is lower than that of the traditional micro-phase shifting method. First, a frequency selection rule is developed in combination with the micro-phase rule to design the frequencies of the proposed phase measuring profilometry. The frequency rule is obtained by analysing the uncertainty of the wrapped phase caused by intensity noise. Then, phase unwrapping is regarded as a congruence problem, and the closed-form robust Chinese remainder theorem algorithm is adopted to determine the correspondence. Finally, the comparative experiments are conducted on a projector-camera system. Experimental results show that the effects of global illumination can be effectively reduced with the proposed phase measuring profilometry, and the proposed frequency selection rule is valid. In addition, the performance of the robust Chinese remainder theorem in addressing the phase error is better than that of traditional Chinese remainder theorem. Furthermore, the unwrapping accuracy can nearly reach 100% if the frequency selection rule is satisfied. Otherwise, the performance degrades.

Invariants of Riemannian curves in dimensions 2 and 3

In this article, a complete and geometrical description of minimal sets of differential invariants in 2- and 3-dimensional Riemannian manifolds is given in terms of the dimension of the isometry group. These invariants provide a solution to the (local) problem of congruence of curves so that a final generalization of Frenet's theory in low dimensional manifolds is reached.

Distributed Angle Estimation by Multiple Frequencies Synthetic Array in Wireless Sensor Localization System

In this paper, we address the problem of distributed angle estimation in wireless sensor localization system. Given that the practical limitations on size and cost, i.e., anchor node cannot equip a complicated antenna or antenna array, we devise an alternative measure based on a fixed-spacing two-antenna equipment. Through the multiple frequencies tuning, a virtual non-uniform linear array, called multiple frequencies synthetic array (MFSA), can be rebuilt independently at each sensor node. We first provide in theory the angle unambiguity conditions for such virtual array and then propose two different algorithms to achieve the distributed angle of departure (AOD) estimation. The first algorithm is based on the spectral searching technique, which is an improved version of the conventional rank reduction estimator (RARE) and has the same performance but less computational complexity. To further alleviate the computational burden at sensor node end, we convert the above angle estimation into a congruence problem and provide another closed-form solution based on Chinese remainder theorem (CRT). We also derive the Cramer-Rao bound for the MFSA and demonstrate theoretically that the latter algorithm from the perspective of cumulative circular distance is suboptimal when compared with the former one. Numerical examples are provided to show the validity of the proposed algorithms and the corresponding conclusions.

Quantitative panbiogeography: was the congruence problem solved?

Panbiogeography represents the spatial congruence among species distributions by means of generalized tracks. Some critics have suggested the method fails to objectively evaluate congruence, being neither repeatable nor falsifiable. The MartiTracks software was proposed to address spatial congruence using geometric properties as a counterpoint to the manual procedures so far employed in generalized track obtainment. To evaluate whether MartiTracks is a reliable alternative to the congruence problem in the quantitative panbiogeographic approach, we tested the software parameters with three analysis schemes under two real datasets. Then, we proceeded to a comparison of the results to those produced from Parsimony Analysis of Endemicity (PAE) and Clique Analysis, two quantitative methods which are based in predefined biogeographic areas or in the employment of grid cells. For PAE we used both analytical units, while Clique Analysis was restricted to grid cells. Through this, we aimed to comparatively evaluate the criteria of spatial congruence in different approaches. For each dataset and method, significantly different tracks resulted, highlighting the disparate congruence criteria among panbiogeographic approaches. Despite PAE ending up as the most reliable of the tools tested, it is still far from solving panbiogeographic congruence. The main focus of this paper, MartiTracks, is indeed a tool that makes minimum spanning tree construction a repeatable and easy-to-visualize process, but stumbles upon its obscure procedures of generalized track obtainment, congruence criteria, subjective parameter definition, the unclear implications of employing said parameters, and dubious results. Our results suggest that the subjectivity of the parameter setup process substantially influences the results, biasing them to the user-desired level of congruence. That the software produces fast and easy-to-visualize results does not make it a definitive solution to the problem of quantitative panbiogeographic approaches.

On Local Congruence of Immersions in Homogeneous or Nonhomogeneous Spaces

We show how to find a complete set of necessary and sufficient conditions that solve the fixed-parameter local congruence problem of immersions in $G$-spaces, whether homogeneous or not, provided that a certain $k^{\rm th}$ order jet bundle over the $G$-space admits a $G$-invariant local coframe field of constant structure. As a corollary, we note that the differential order of a minimal complete set of congruence invariants is bounded by $k+1$. We demonstrate the method by rediscovering the speed and curvature invariants of Euclidean planar curves, the Schwarzian derivative of holomorphic immersions in the complex projective line, and equivalents of the first and second fundamental forms of surfaces in ${\mathbb R}^3$ subject to rotations

Nonfinancial Performance Measures and the Incentive Intensity of CEO Bonus Contracts

Firms add nonfinancial measures to their CEO bonus contracts when a sole reliance on financial measures would not be informative about managerial effort. In this paper, we argue that adding nonfinancial measures to CEO contracts may not resolve the congruence problems that would originate from a sole reliance on financial measures. Thus, this paper investigates the assertion that companies optimally provide weak incentives if they lack undistorted performance measures (Baker, 2002). Using a sample of 164 Dutch firms listed on the Amsterdam Stock Exchange and explicitly taking into account the joint nature of decisions to assign a weight to nonfinancial measures and to select the appropriate incentive intensity through a 2SLS model, we find that firms that seek to provide strong incentives decrease the relative weight of nonfinancial measures in CEO bonus contracts. This coincides with prior literature that suggests that firms adjust for items in their reported earnings to improve their financial summary performance measure.

A Congruence Problem for Polyhedra

(2010). A Congruence Problem for Polyhedra. The American Mathematical Monthly: Vol. 117, No. 3, pp. 232-249.

Similarity of some dual operators in characteristic two

Let k be a field of characteristic two, with involution x ↦ x ¯ . Let ( V , · ) be a finite dimensional Hermitian space over k and Λ : V → V a linear operator whose dual is Λ + 1 . We prove that ϕ Λ ϕ - 1 = Λ + 1 , where ϕ is an isometry and ϕ 2 = 1 . If E is a given subspace of V , then ϕ can also be chosen to stabilize E , but the equality ϕ Λ ϕ - 1 = Λ + 1 is only true modulo a combination of certain bracket operators. As a corollary, we solve the following congruence problem. Given a square matrix A over k , there is a non-singular matrix S satisfying A T = S ¯ T AS and S S ¯ = 1 .

On the logarithmic factor in error term estimates in certain additive congruence problems

We remove logarithmic factors in error term estimates in asymptotic formulas for the number of solutions of a class of additive congruences modulo a prime number.

On character sums and the exceptional set of a congruence problem

We prove an estimate of character sums. This bound and the method of solving multiplicative ternary problems are used to obtain new results about the cardinality of an exceptional set of a congruence problem modulo a prime p. In particular, we show that “almost all” residue classes modulo p are representable in the form xy(modp), where max{x,y}≪p58+ɛ.

Noncongruence subgroups in H(2)

We study the congruence problem for subgroups of the modular group that appear as Veech groups of square-tiled surfaces in the minimal stratum of abelian differentials of genus two.

The congruence problem in John Holland's theory of vocational decisions

John Holland's theory of vocational choice has been a dominant one in careers psychology for many years, especially in North America. A key construct in the theory is congruence between person and environment. Yet research has failed to find as strong a link as might be expected between congruence and outcomes such as satisfaction and performance. This could present a major challenge to the theory. Fourteen possible reasons for the weak associations between congruence and outcome measures are identified and discussed under three broad headings: the theory, the research and the world. It is concluded that the most important reasons are (1) that Holland's measures of people and environments partially neglect some important constructs; (2) that environments have not been conceptualized or measured entirely appropriately; and (3) the data that are used in the calculation of congruence indices are insufficiently precise or comprehensive. It is suggested that Holland's theory and associated measures should be developed further, and that the processual elements of it need more attention.