Showing papers on "Class (philosophy) published in 2018"

Distribution-specific hardness of learning neural networks

Abstract: Although neural networks are routinely and successfully trained in practice using simple gradient-based methods, most existing theoretical results are negative, showing that learning such networks is difficult, in a worst-case sense over all data distributions. In this paper, we take a more nuanced view, and consider whether specific assumptions on the "niceness" of the input distribution, or "niceness" of the target function (e.g. in terms of smoothness, non-degeneracy, incoherence, random choice of parameters etc.), are sufficient to guarantee learnability using gradient-based methods. We provide evidence that neither class of assumptions alone is sufficient: On the one hand, for any member of a class of "nice" target functions, there are difficult input distributions. On the other hand, we identify a family of simple target functions, which are di_cult to learn even if the input distribution is "nice". To prove our results, we develop some tools which may be of independent interest, such as extending Fourier-based hardness techniques developed in the context of statistical queries (Blum et al., 1994), from the Boolean cube to Euclidean space and to more general classes of functions.

Normal generators for mapping class groups are abundant

Abstract: We provide a simple criterion for an element of the mapping class group of a closed surface to have normal closure equal to the whole mapping class group. We apply this to show that every nontrivial periodic mapping class that is not a hyperelliptic involution is a normal generator for the mapping class group when the genus is at least 3. We also give many examples of pseudo-Anosov normal generators, answering a question of D. D. Long. In fact we show that every pseudo-Anosov mapping class with stretch factor less than $\sqrt{2}$ is a normal generator. Even more, we give pseudo-Anosov normal generators with arbitrarily large stretch factors and arbitrarily large translation lengths on the curve graph, disproving a conjecture of Ivanov.

Two simultaneous actions of big mapping class groups

Abstract: We study two actions of big mapping class groups. The first is an action by isometries on a Gromov-hyperbolic graph. The second is an action by homeomorphisms on a circle in which the vertices of the graph naturally embed. The first two parts of the paper are devoted to the definition of objects and tools needed to introduce these two actions; in particular, we define and prove the existence of equators for infinite type surfaces, we define the hyperbolic graph and the circle needed for the actions, and we describe the Gromov-boundary of the graph using the embedding of its vertices in the circle. The third part focuses on some fruitful relations between the dynamics of the two actions. For example, we prove that loxodromic elements (for the first action) necessarily have rational rotation number (for the second action). In addition, we are able to construct non trivial quasimorphisms on many subgroups of big mapping class groups, even if they are not acylindrically hyperbolic.

Graphon games: A statistical framework for network games and interventions

Abstract: In this paper, we present a unifying framework for analyzing equilibria and designing interventions for large network games sampled from a stochastic network formation process represented by a graphon. We first introduce a new class of infinite population games, termed graphon games, where a continuum of heterogeneous agents interact according to a graphon. After studying properties of equilibria in graphon games, we show that graphon equilibria can approximate equilibria of large network games sampled from the graphon. We next show that, under some regularity assumptions, the graphon approach enables the design of asymptotically optimal interventions via the solution of an optimization problem with much lower dimension than the one based on the entire network structure. We illustrate our framework on a synthetic dataset of rural villages and show that the graphon intervention can be computed efficiently and based solely on aggregated relational data.

Renormalized oscillation theory for linear Hamiltonian systems on [0,1] via the Maslov index

Abstract: Working with a general class of linear Hamiltonian systems on $[0, 1]$, we show that renormalized oscillation results can be obtained in a natural way through consideration of the Maslov index associated with appropriately chosen paths of Lagrangian subspaces of $\mathbb{C}^{2n}$. We verify that our applicability class includes Dirac and Sturm-Liouville systems, as well as a system arising from differential-algebraic equations for which the spectral parameter appears nonlinearly.

A Framework for Tackling Myopia in Concept Learning on the Web of Data

Abstract: A prominent class of supervised methods for the representations adopted in the context of the Web of Data are designed to solve concept learning problems. Such methods aim at approximating an intensional definition for a target concept from a set of individuals of a target knowledge base. In this scenario, most of the well-known solutions exploit a separate-and-conquer approach: intuitively, the learning algorithm builds an intensional definition by repeatedly specializing a partial solution with the aim of covering the largest number of positive examples as possible. Essentially such a strategy can be regarded as a form of hill-climbing search that can produce sub-optimal solutions. To cope with this problem, we propose a novel framework for the concept learning problem called DL-Focl. Three versions of this algorithmic solution, built upon DL-Foil, have been designed to tackle the inherent myopia of the separate-and-conquer strategies. Their implementation has been empirically tested against methods available in the DL-Learner suite showing interesting results.

Classical simulation of quantum circuits by half Gauss sums

Abstract: We give an efficient algorithm to evaluate a certain class of exponential sums, namely the periodic, quadratic, multivariate half Gauss sums. We show that these exponential sums become $\#\mathsf{P}$-hard to compute when we omit either the periodic or quadratic condition. We apply our results about these exponential sums to the classical simulation of quantum circuits and give an alternative proof of the Gottesman-Knill theorem. We also explore a connection between these exponential sums and the Holant framework. In particular, we generalize the existing definition of affine signatures to arbitrary dimensions and use our results about half Gauss sums to show that the Holant problem for the set of affine signatures is tractable.

Multimodal One-Shot Learning of Speech and Images

Abstract: Imagine a robot is shown new concepts visually together with spoken tags, e.g. "milk", "eggs", "butter". After seeing one paired audio-visual example per class, it is shown a new set of unseen instances of these objects, and asked to pick the "milk". Without receiving any hard labels, could it learn to match the new continuous speech input to the correct visual instance? Although unimodal one-shot learning has been studied, where one labelled example in a single modality is given per class, this example motivates multimodal one-shot learning. Our main contribution is to formally define this task, and to propose several baseline and advanced models. We use a dataset of paired spoken and visual digits to specifically investigate recent advances in Siamese convolutional neural networks. Our best Siamese model achieves twice the accuracy of a nearest neighbour model using pixel-distance over images and dynamic time warping over speech in 11-way cross-modal matching.

Addition-deletion theorem for free hyperplane arrangements and combinatorics

Abstract: In the theory of hyperplane arrangements, the most important and difficult problem is the combinatorial dependency of several properties. In this atricle, we prove that Terao's celebrated addition-deletion theorem for free arrangements is combinatorial, i.e., whether you can apply it depends only on the intersection lattice of arrangements. The proof is based on a classical technique. Since some parts are already completed recently, we prove the rest part, i.e., the combinatoriality of the addition theorem. As a corollary, we can define a new class of free arrangements called the additionally free arrangement of hyperplanes, which can be constructed from the empty arrangement by using only the addition theorem. Then we can show that Terao's conjecture is true in this class. As an application, we can show that every ideal-Shi arrangement is additionally free, implying that their freeness is combinatorial.

Teaching digital electronics course for electrical engineering students in cognitive domain

Abstract: Digital electronics course is one of the very fundamental courses for the students of undergraduate programme of electrical and electronic engineering (EEE) and the other undergraduate engineering disciplines. Therefore, ‘digital electronics’ shall be taught effectively, so that students can apply the knowledge learned to solve their real-life engineering problems. A teacher needs to adopt new teaching methodologies to attract current generation of students, and thus, to prepare them with practical knowledge and skills. Skills in the cognitive domain of Bloom’s taxonomy revolve around knowledge, comprehension and critical thinking of a particular topic. This makes teaching and learning more effective and efficient. In this paper, the teaching method of ‘digital electronics’ course for the undergraduate EEE students in the cognitive domain has been described with an example. Class performance evaluation in two different cohorts shows that the students’ results improve after using this approach.Keywords: Bloom’s taxonomy, cognitive domain, digital electronics course, teaching methods.

Geometry of the Phase Retrieval Problem

Abstract: One of the most powerful approaches to imaging at the nanometer or subnanometer length scale is coherent diffraction imaging using X-ray sources. For amorphous (non-crystalline) samples, the raw data can be interpreted as the modulus of the continuous Fourier transform of the unknown object. Making use of prior information about the sample (such as its support), a natural goal is to recover the phase through computational means, after which the unknown object can be visualized at high resolution. While many algorithms have been proposed for this phase retrieval problem, careful analysis of its well-posedness has received relatively little attention. In this paper, we show that the problem is, in general, not well-posed and describe some of the underlying issues that are responsible for the ill-posedness. We then show how this analysis can be used to develop experimental protocols that lead to better conditioned inverse problems.

A K-theoretic Fulton class

Abstract: Fulton defined classes in the Chow group of a quasi-projective scheme $M$ which reduce to its Chern classes when $M$ is smooth. When $M$ has a perfect obstruction theory, Siebert gave a formula for its virtual cycle in terms of its total Fulton class. We describe K-theory classes on $M$ which reduce to the exterior algebra of differential forms when $M$ is smooth. When $M$ has a perfect obstruction theory, we give a formula for its K-theoretic virtual structure sheaf in terms of these classes.

Implementation and Analysis of Combined Machine Learning Method for Intrusion Detection System

Abstract: As one of the security components in Network Security Monitoring System, Intrusion Detection System (IDS) is implemented by many organizations in their networks to detect and address the impact of network attacks. There are many machine-learning methods that have been widely developed and applied in the IDS. Selection of appropriate methods is necessary to improve the detection accuracy in the application of machine-learning in IDS. In this research we proposed an IDS that we developed based on machine learning approach. We use 28 features subset without content features of Knowledge Data Discovery (KDD) dataset to build machine learning model. From our analysis and experiment we get 28 features subset of KDD dataset that are most likely to be applied for the IDS in the real network. The machine learning model based on this 28 features subset obtained 99.9% accuracy for both two-class and multiclass classification. From our experiments using the IDS we have developed show good performance in detecting attacks on real networks.

Integral functionals for spectrally positive Levy processes

Abstract: We find necessary and sufficient conditions for almost sure finiteness of integral functionals of spectrally positive Levy processes Via Lamperti type transforms, these results can be applied to obtain new integral tests on extinction and explosion behaviors for a class of continuous-state nonlinear branching processes

Disjointness of M\"{o}bius from asymptotically periodic functions

Abstract: In this paper, we investigate asymptotically periodic functions from the point of view of operator algebra and dynamical systems. To study the Mobius disjointness of these functions, we prove a general result on the averages of multiplicative functions in short arithmetic progressions. As an application, we show that Sarnak's Mobius Disjointness Conjecture holds for certain topological dynamical systems.

Counter Machines and Distributed Automata

Abstract: We prove the equivalence of two classes of counter machines and one class of distributed automata. Our counter machines operate on finite words, which they read from left to right while incrementing or decrementing a fixed number of counters. The two classes differ in the extra features they offer: one allows to copy counter values, whereas the other allows to compute copyless sums of counters. Our distributed automata, on the other hand, operate on directed path graphs that represent words. All nodes of a path synchronously execute the same finite-state machine, whose state diagram must be acyclic except for self-loops, and each node receives as input the state of its direct predecessor. These devices form a subclass of linear-time one-way cellular automata.

Game semantics for dependent types

Abstract: We present a model of dependent type theory ( DTT ) with Π-, 1-, Σ- and intensional Id -types, which is based on a slight variation of the (call-by-name) category of AJM-games and history-free winning well-bracketed strategies. The model satisfies Streicher's criteria of intensionality and refutes function extensionality. The principle of uniqueness of identity proofs is satisfied. We show it contains a submodel as a full subcategory which gives a faithful interpretation of DTT with Π-, 1-, Σ- and intensional Id -types and, additionally, finite inductive type families. This smaller model is fully (and faithfully) complete with respect to the syntax at the type hierarchy built without Id -types, as well as at the more general class of types where we allow for one strictly positive occurrence of an Id -type. Definability for the full type hierarchy with Id -types remains to be investigated.

(Semi)-global analytic hypoellipticity for a class of “sums of squares” which fail to be locally analytic hypoelliptic

Abstract: The global and semi-global analytic hypoellipticity on the torus is proved for two classes of sums of squares operators, introduced in [1] and [2], satisfying the Hörmander condition and which fail to be neither locally nor microlocally analytic hypoelliptic.

Poverty, social mobility, and the middle class: The case of South Africa

Abstract: The wave of upbeat stories on the developing world's emerging middle class has reinvigorated a debate on how social class in general and the middle class in particular ought to be defined and empirically measured. With the aim of adding clarity to this debate, this dissertation provides a structured overview of a wide array of definitions of the middle class that have been suggested in the economics literature, and assesses their strengths and shortcomings using South Africa as a case study. Contrary to most standard approaches in the economic realm, the main argument this dissertation makes is that – in contexts marked by high inequality and socio-economic insecurity – social class is insufficiently understood by a person’s current standard of living alone. Addressing this concern, a novel conceptual framework is proposed that takes the unequal distribution of chances of upward and downward social mobility explicitly into consideration when defining class categories. It compares the proposed approach to those that have been suggested in the previous literature, investigates the sources of upward and downward mobility, and illustrates the main messages that can be learnt from linking the demarcation of social strata to an in-depth analysis of mobility patterns. Four main messages emerge from the analysis presented in this dissertation: First, the chosen indicator(s) of social class will certainly make a clear difference not only with respect to the estimated size and growth of the middle class, but especially with regard to its characteristics, needs, and relationship to other economic or political. Second, the notion of economic security and stability is central to the social and political meanings of being middle class. The stable middle class that is identified using (in-)vulnerability to poverty as a class-defining criterion will generally be much smaller than approaches relying on less demanding criteria suggest. For the specific case of South Africa, this research shows that only one out of four persons can be considered stably middle class or elite. Conversely, about half of the population are locked in persistent structural poverty. Third, if the growth of a stable middle class is a desired development outcome and focus of government policy, then an explicit focus on the stability and quality of employment is essential. Not only the lack of jobs, but also the prevalence of casual and precarious forms of work impede the development of a stable middle class. Lastly, there is an important extent of heterogeneity in the political attitudes of the middle class, which is determined by whether people perceive themselves as winners or losers under the existing political system. While those who perceive themselves as being downwardly mobile display signs of political resignation, those people who perceive themselves as upwardly mobile tend, on average, to be less concerned with corruption and more tolerant of government constraints on political freedoms.

Abelian capitulation of ray class groups

Abstract: Building on Bosca's method, we extend to tame ray class groups the results on capitulation of ideals of a number field by composition with abelian extensions of a subfield first studied by Gras. More precisely, for every extension of number fields K/k, where at least one infinite place splits completely, and every squarefree divisor m of K, we prove that there exist infinitely many abelian extensions F/k such that the ray class group mod m of K capitulates in KF. As a consequence we generalize to tame ray class groups the results of Kurihara on triviality of class groups for maximal abelian pro-extensions of totally real number fields.

Kemampuan Representasi Matematis Siswa SMP Kelas VIII pada Materi Sistem Persamaan Linear Dua Variabel dengan Pendekatan Kontekstual

Abstract: This study aims to examine the improvement of students' representation ability of Class VIII on the material of two-variable linear equation system through contextual approach. This type of research is classroom action research. The method of this research is qualitative descriptive. This research was conducted on Grade VIII-A students of SMP Mahardhika in the academic year 2017/2018 with 39 students. The instrument used is a student's mathematical representation test, cycles I and II tests (after giving of action), and an observation sheet for teachers and students to conditions of action implementation. The results of this study indicate that the aspect of mathematical representation ability of students has increased because of the problems tested in each test, the more students who score above the KKM. Based on the work indicator, it is concluded that the mathematical representation ability of grade VIII-A students of SMP Mahardhika Batujajar on two-variable linear equation system can be improved through contextual approach.

Enumerating Isotopy Classes of Tilings guided by the symmetry of Triply-Periodic Minimal Surfaces

Abstract: We present a technique for the enumeration of all isotopically distinct ways of tiling a hyperbolic surface of finite genus, possibly nonorientable and with punctures and boundary. This provides a generalization of the enumeration of Delaney-Dress combinatorial tiling theory on the basis of isotopic tiling theory. To accomplish this, we derive representations of the mapping class group of the orbifold associated to the symmetry group in the group of outer automorphisms of the symmetry group of a tiling. We explicitly give descriptions of certain subgroups of mapping class groups and of tilings as decorations on orbifolds, namely those that are commensurate with the Primitive, Diamond and Gyroid triply-periodic minimal surfaces. We use this explicit description to give an array of examples of isotopically distinct tilings of the hyperbolic plane with symmetries generated by rotations, outlining how the approach yields an unambiguous enumeration.

Tame hereditary path algebras and amenability

Abstract: In this note we are concerned with the notion of amenable representation type as defined in a recent paper by Gabor Elek. Roughly speaking, an algebra is of amenable type if for all $\varepsilon > 0$, every finite-dimensional module has a submodule which is a direct sum of modules which are small with respect to $\varepsilon$ such that the quotient is also small in that respect. We will show that the tame hereditary path algebras of quivers of extended Dynkin type over any field $k$ are of amenable type, thus extending a conjecture in the aforementioned paper to another class of tame algebras. In doing so, we avoid using already known results for string algebras. We also show that path algebras of wild acyclic quivers over finite fields are not amenable.

Three Approaches for Mining Definitions from Relational Data in the Web of Data

Abstract: In this paper we study a classification process on relational data that can be applied to the web of data We start with a set of objects and relations between objects, and extensional classes of objects We then study how to provide a definition to classes, ie to build an intensional description of the class, wrt the relations involving class objects To this end, we propose three different approaches based on Formal Concept Analysis (FCA), redescription mining and Minimum Description Length (MDL) Relying on some experiments on RDF data from DBpedia, where objects correspond to resources, relations to predicates and classes to categories, we compare the capabilities and the comple-mentarity of the three approaches This research work is a contribution to understanding the connections existing between FCA and other data mining formalisms which are gaining importance in knowledge discovery, namely redescription mining and MDL

A Conceptual Restructuring of Spatial Motion Expressions in Chinese L2.

Abstract: This paper focuses on the patterns in the encoding of spatial motion events that play a major role in the acquisition of these type of expressions. The goal is to single out the semantic contribution of the linguistic items which surface in Chinese locative constructions. In this way, we intend to provide learners with an account of the spatial representation encoded in the Chinese language. In fact, Chinese grammar is often perceived as idiosyncratic, thus generating a frustration that turns into learned helplessness (Maier and Seligman, 1976). We will analyze Talmy (2000a,b) framework under the light of investigations such as Landau and Jackendoff (1993), Svenonius (2004, 2006, 2007), and Terzi (2010). It will be shown that in Chinese locative structures, the Axial Part information is signaled by localizers and can be specified only when the Ground is considered as an object with "axially determined parts" (Landau and Jackendoff, 1993). Thus, we will elaborate on present account on the localizer's function (Peyraube, 2003; Lamarre, 2007; Lin, 2013) by showing that the localizer highlights an axially determined part within a reference object, consistently with Terzi (2010) definition of Place, and with Wu (2015) decomposition of Place into Ground and Axial Part. Moreover, it will be shown that the preposition zai 'at' encodes a Locative type of Motion event (Talmy, 2000b), thus, it is not semantically vacuous. Other categories will be presented, such as the semantic class of locational verbs (Huang, 1987). We will indicate the contexts wherein such notions can trigger the conceptual restructuring which enables adult learners to switch from L1 "thinking for speaking" to L2 "thinking for speaking" (Slobin, 1987). The paper is structured as follows: Section "Introduction" provides introduction to the theme; Section "Theoretical Framework" includes a surveys on the semantic and syntactic decompositions of spatial motion expressions; Section "Discussion" offers an account of the instantiation; the findings and the relevant pedagogical implications are presented in Section "Findings."

Lebesgue's Density Theorem and definable selectors for ideals.

Abstract: We introduce a notion of density point and prove results analogous to Lebesgue's density theorem for various well-known ideals on Cantor space and Baire space. In fact, we isolate a class of ideals for which our results hold. In contrast to these results, we show that there is no reasonably definable selector that chooses representatives for the equivalence relation on the Borel sets of having countable symmetric difference. In other words, there is no notion of density which makes the ideal of countable sets satisfy an analogue to the density theorem. The proofs of the positive results use only elementary combinatorics of trees, while the negative results rely on forcing arguments.

Methods and systems for implied graph patterns in property chains

Abstract: A system and a method including accessing a semantic model having a grammar syntax supporting an expression including a combination of at least one of a semantic model class and an instance of a semantic model class; specifying at least one missing property specification for at least one of a semantic model class and an instance of a semantic model class, including constraints for a use of the at least one missing property; adding the at least one missing property specification to the semantic model, the at least one missing property specification added to the semantic model to be referenced in a validation and translation of an expression including a combination of at least one of the class and the instance of a class having one of the at least one missing property specified therewith; and generating a record of the semantic model including the at least one missing property specification added thereto.

Analisis kemampuan komunikasi matematis dan keaktifan siswa sma dengan pendekatan problem posing

Abstract: The background of this research problem, starting from the still low ability of mathematical communication and the activity of high school students. The purpose of this research is to describe the improvement of mathematical communication ability and activity of class X students of SMA Muhamadiyah 1 Cimahi. Design Research conducted a classroom study using John Elliot's model. The research flow has two cycles, each cycle consisting of planning, execution, observation and reflection. The result of this research is that there is improvement of mathematical communication ability and activeness by applying problem posing approach on learning mathematics about SPLTV in SMA Muhammadiyah 1 Cimahi class X, for the improvement of mathematical communication ability viewed based on percentage of students whose value is below KKM, equal to KKM, and above the KKM sequentially respectively by 9.68%, 54.84%, and 96.77%. To increase student activeness can be seen based on percentage of students who have active active value and very active in cycle I and cycle II, respectively equal to 35,48% and 93,54%.

Entity class determining method and device

Abstract: The invention provides an entity class determining method and device in a knowledge graph. The method comprises the steps of acquiring a candidate data pair set, wherein the candidate data pair set comprises at least one candidate data pair, each piece of data of the candidate data pair comprises at least one entity and at least one class; determining, based on attribute information of the entity,attribute value of the entity and/or attribute information of the class, whether at least one entity included in the at least one candidate data pair belongs to at least one class included in the candidate data pair, and if yes, labeling the at least one class as a class of the at least one entity. Through adoption of the method, the entity class is determined, entity classes are increased, and/or entity class accuracy is improved.