Intersection Of Classes Research Articles

Contact graphs of boxes with unidirectional contacts

This paper is devoted to the study of particular geometrically defined intersection classes of graphs. Those were previously studied by Magnant and Martin, who proved that these graphs have arbitrary large chromatic number, while being triangle-free. We give several structural properties of these graphs, and we raise several questions.

A Simple and Practical Method for Reducing the Disparate Impact of Differential Privacy

Differentially private (DP) mechanisms have been deployed in a variety of high-impact social settings (perhaps most notably by the U.S. Census). Since all DP mechanisms involve adding noise to results of statistical queries, they are expected to impact our ability to accurately analyze and learn from data, in effect trading off privacy with utility. Alarmingly, the impact of DP on utility can vary significantly among different sub-populations. A simple way to reduce this disparity is with stratification. First compute an independent private estimate for each group in the data set (which may be the intersection of several protected classes), then, to compute estimates of global statistics, appropriately recombine these group estimates. Our main observation is that naive stratification often yields high-accuracy estimates of population-level statistics, without the need for additional privacy budget. We support this observation theoretically and empirically. Our theoretical results center on the private mean estimation problem, while our empirical results center on extensive experiments on private data synthesis to demonstrate the effectiveness of stratification on a variety of private mechanisms. Overall, we argue that this straightforward approach provides a strong baseline against which future work on reducing utility disparities of DP mechanisms should be compared.

Trapped in Place? Ethnic and Educational Heterogeneity in Residential Mobility and Integration of Young Adults in Brussels

Spatial assimilation theory asserts that immigrants’ socioeconomic progress leads to residential adaptation and integration. This association has proven robust in USA and European urban areas through much of the twentieth century, but drastic change of ethnic and class compositions yet persistent (neighbourhood) inequality in the urban landscape urge us to reconsider the dynamic interaction between stability and change. In this study, we investigate to what extent education shapes residential mobility differently for young adults with varying ethnic and social origins. Focussing on Brussels, we use multinomial logistic regressions on linked longitudinal population-based censuses from 1991 and 2001 and register data for the period 2001–2006. Analyses show that dispersal away from poor inner-city neighbourhoods appears least likely for the offspring of poor low-educated non-Western households, regardless of their own educational attainment. While our approach roughly confirms traditional arguments of socio-spatial integration, it also reveals how educational success generates opportunities to escape poor neighbourhoods for some but not for others. With this, it points at the subtle ways in which factors and mechanisms in traditional spatial assimilation theory affect residential behaviour of young adults over their life course, at the intersection of specific locales, ethnic groups, social classes and generations.

Design of Safety Petri Net Controllers for Deadlock Prevention at a Class of Road Intersections

Design of Safety Petri Net Controllers for Deadlock Prevention at a Class of Road Intersections

Framed duality and mirror symmetry for toric complete intersections

This paper is devoted to systematically extend f-mirror symmetry between families of hypersurfaces in complete toric varieties, as introduced in [17], to families of complete intersections subvarieties. Namely, f-mirror symmetry is induced by framed duality of framed toric varieties extending Batyrev-Borisov polar duality between Fano toric varieties. Framed duality has been defined and essentially well described for families of hypersurfaces in toric varieties in the previous [17]. Here it is developed for families of complete intersections, allowing us to strengthen some previous results on hypersurfaces. In particular, the class of projective complete intersections and their mirror partners are studied in detail. Moreover, a (generalized) Landau-Ginzburg/Complete-Intersection correspondence is discussed, extending to the complete intersection setup the LG/CY correspondence firstly studied Chiodo-Ruan and Krawitz.

Balanced covering arrays: A classification of covering arrays and packing arrays via exact methods

AbstractIn this paper we investigate the intersections of classes of covering arrays (CAs) and packing arrays (PAs). The arrays appearing in these intersections obey to upper and lower bounds regarding the appearance of tuples in sub‐matrices—we call these arrays balanced covering arrays. We formulate and formalize first observations for which upper and lower bounds on the appearance of tuples it is of interest to consider these intersections of CAs and PAs. Outside of these bounds the intersections will be either empty, for the case of too restrictive constraints, or equal to the maximum element in the emerging lattices, for the case of too weak constraints. We present a column extension algorithm for classification of nonequivalent balanced CAs that uses a SAT solver or a pseudo‐Boolean (PB) solver to compute the columns suitable for array extension together with a lex‐leader ordering to identify unique representatives for each equivalence class of balanced CAs. These computations bring to light a dissection of classes of CAs that is partially nested due to the nature of the considered intersections. These dissections can be trivial, containing only a single type of balanced CAs, or can also appear as highly structured containing multiple nested types of balanced CAs. Our results indicate that balanced CAs are an interesting class of designs that is rich of structure.

The Structure of Weight and Function Classes With Coprime Bases

Abstract In a recent work of Anderson and Hu, the authors constructed a measure that was p-adic and q-adic doubling, for any primes p and q, yet not doubling. This work relied heavily on a developed number theory framework. Here we develop this framework further, which yields a measure that is m-adic and n-adic doubling for any coprime $m,n$, yet not doubling. Additionally, we show several new applications to the intersection of weight and function classes.

Information-Extreme Machine Learning of Wrist Prosthesis Control System Based on the Sparse Training Matrix

The article considers the problem of machine learning of a wrist prosthesis control system with a non-invasive biosignal reading system. The task is solved within the framework of information-extreme intelligent data analysis technology, which is based on maximizing the system’s information productivity in machine learning. The idea of information-extreme machine learning of the control system for recognition of electromyographic biosignals, as in artificial neural networks, consists in adapting the input information description to the maximum total probability of making correct classification decisions. However, unlike neuro-like structures, the proposed method was developed within a functional approach to modeling the cognitive processes of the natural intelligence of forming and making classification decisions. As a result, the proposed method acquires the properties of adaptability to the intersection of classes in the space of recognition features and flexibility when retraining the system due to the recognition class alphabet expansion. In addition, the decision rules constructed within the framework of the geometric approach are practically invariant to the multidimensionality of the space of recognition features. The difference between the developed method and the well-known methods of information-extreme machine learning is the use of a sparse training matrix, which allows for reducing the degree of intersection of recognition classes significantly. The optimization parameter of the input information description, the training dataset, is the quantization level of electromyographic biosignals. As an optimization criterion is considered the modified Kullback information measure. The proposed machine learning algorithm results are shown in the example of recognition of six finger movements and wrist.

Intersection Safety Assessment Using Video-Based Traffic Conflict Analysis: The Case Study of Thailand

In the road transport network, intersections are among the most critical locations leading to a risk of death and serious injury. The traditional methods to assess the safety of intersections are based on statistical analyses that require crash data. However, such data may be under-reported and omit important crash-related factors. The conventional approaches, therefore, are not easily applied to making comparisons of intersection designs under different road classifications. This study developed a risk-based approach that incorporates video-based traffic conflict analysis to investigate vehicle conflicts under mixed traffic conditions including motorcycles and cars in Thailand. The study applied such conflict data to assess the risk of intersections in terms of time-to-collision and conflict speed. Five functional classes of intersections were investigated, including local-road/local-road, local-road/collector, collector/arterial, collector/collector, and arterial/arterial intersections. The results showed that intersection classes, characteristics, and control affect the behavior of motorists and the safety of intersections. The results found that the low-order intersections with stop/no control are high risks due to the short time-to-collision of motorcycle-related conflicts. They generate frequent conflicts with low chance of injury. The high-order intersections with signal control are high risks due to high conflicting speeds of motorcycle–car conflicts. They generate few conflicts but at a high chance of injury. The study presents the applicability of video-based traffic conflict analysis for systematically estimating the crash risk of intersections. The risk-based approach can be deemed as a supplement indicator in addition to limited crash data to evaluate the safety of intersections. However, future research is needed to explore the potential of other road infrastructure under different circumstances.

LARGE INTERSECTION PROPERTIES FOR LIMSUP SETS GENERATED BY RECTANGLES IN COMPACT METRIC SPACES

The large intersection classes in real Euclidean spaces have been introduced by Falconer in 1985. First, we generalize Falconer’s large intersection classes to compact metric spaces and show that these classes are closed under countable intersections. Next, we prove that the limsup sets generated by rectangles in a compact metric space enjoy this intersection property under certain full Hausdorff measure assumptions. We also apply our results to high-dimensional Diophantine approximation on fractals.

Scheduling of Flyover at Grade Intersection for Amravati

This work concerns the effective planning of flight at the intersection of classes under a mixed traffic environment. From the results and simulations performed in the SIDRA Intersection software, different points are observed. This work consists of a proposed crossing in Rajamal Square, Amravati. The area is highly populated, and this place offers the need for a good quality intersection. The graph shows that the turn of the 95% of the worst lane of the car per year increases as the year increases. The maximum value is 0.011. The graph shows that the stopping speed, which is detected, decreases as the year increases. The minimum value of the stopping speed is 0.5485. The graph shows that productivity increases over time. The maximum value of the performance index is 0.30.

Elliptic genera of level N for complete intersections

We focus on the elliptic genera of level N at the cusps of a congruence subgroup for any complete intersection. Writing the first Chern class of a complete intersection as a product of an integral coefficient c1 and a generator of the 2nd integral cohomology group, we mainly discuss the values of the elliptic genera of level N for the complete intersection in the cases of c1 >, =, or < 0. In particular, the values about the Todd genus, Â-genus, and Ak-genus can be derived from the elliptic genera of level N.

New cryptographic hardness for learning intersections of halfspaces over boolean cubes with membership queries

We revisit the PAC learnability of the class of intersections of polynomially many halfspaces over boolean cubes in the membership query model. The previous works (Klivans-Sherstov 2009, Angluin-Kharitonov 1995) imply the unlearnability of this class based on cryptographic assumptions, which is established in the case that the learner cannot generate queries of positive labels. We investigate this issue, focusing on the case that the learner is given representations of input distributions (so it may generate queries of positive and negative labels).Our result is that assuming some new cryptographic primitives, the class is still unlearnable in the query model even if the learner has representations of the distributions. The result is established via a new argument. We show that if the class is learnable, we can come up with a differing-inputs obfuscator, which, however, does not exist given the cryptographic primitives. Thus the hardness result follows from the contradiction.

On classes of life distributions based on the mean time to failure function

AbstractThe performance and effectiveness of an age replacement policy can be assessed by its mean time to failure (MTTF) function. We develop shock model theory in different scenarios for classes of life distributions based on the MTTF function where the probabilities $\bar{P}_k$ of surviving the first k shocks are assumed to have discrete DMTTF, IMTTF and IDMTTF properties. The cumulative damage model of A-Hameed and Proschan [1] is studied in this context and analogous results are established. Weak convergence and moment convergence issues within the IDMTTF class of life distributions are explored. The preservation of the IDMTTF property under some basic reliability operations is also investigated. Finally we show that the intersection of IDMRL and IDMTTF classes contains the BFR family and establish results outlining the positions of various non-monotonic ageing classes in the hierarchy.

On the Optimality of Affine Policies for Budgeted Uncertainty Sets

In this paper, we study the performance of affine policies for a two-stage, adjustable, robust optimization problem with a fixed recourse and an uncertain right-hand side belonging to a budgeted uncertainty set. This is an important class of uncertainty sets, widely used in practice, in which we can specify a budget on the adversarial deviations of the uncertain parameters from the nominal values to adjust the level of conservatism. The two-stage adjustable robust optimization problem is hard to approximate within a factor better than [Formula: see text] even for budget of uncertainty sets in which [Formula: see text] is the number of decision variables. Affine policies, in which the second-stage decisions are constrained to be an affine function of the uncertain parameters provide a tractable approximation for the problem and have been observed to exhibit good empirical performance. We show that affine policies give an [Formula: see text]-approximation for the two-stage, adjustable, robust problem with fixed nonnegative recourse for budgeted uncertainty sets. This matches the hardness of approximation, and therefore, surprisingly, affine policies provide an optimal approximation for the problem (up to a constant factor). We also show strong theoretical performance bounds for affine policy for a significantly more general class of intersection of budgeted sets, including disjoint constrained budgeted sets, permutation invariant sets, and general intersection of budgeted sets. Our analysis relies on showing the existence of a near-optimal, feasible affine policy that satisfies certain nice structural properties. Based on these structural properties, we also present an alternate algorithm to compute a near-optimal affine solution that is significantly faster than computing the optimal affine policy by solving a large linear program.

Isomonodromic deformations of a rational differential system and reconstruction with the topological recursion: The sl2 case

In this paper, we show that it is always possible to deform a differential equation ∂xΨ(x) = L(x)Ψ(x) with L(x)∈sl2(C)(x) by introducing a small formal parameter ℏ in such a way that it satisfies the topological type properties of Bergère, Borot, and Eynard [Annales Henri Poincaré 16(12), 2713–2782 (2015)]. This is obtained by including the former differential equation in an isomonodromic system and using some homogeneity conditions to introduce ℏ. The topological recursion is then proved to provide a formal series expansion of the corresponding tau-function whose coefficients can thus be expressed in terms of intersections of tautological classes in the Deligne–Mumford compactification of the moduli space of surfaces. We present a few examples including any Fuchsian system of sl2(C)(x) as well as some elements of Painlevé hierarchies.

NP-Completeness of the Independent Dominating Set Problem in the Class of Cubic Planar Bipartite Graphs

It is known that the independent dominating set problem is NP-complete both in the class of cubic planar graphs and in the class of cubic bipartite graphs. Still open is the question about the computational complexity of the problem in the intersection of these graph classes. In this article, we prove that the independent dominating set problem is NP-complete in the class of cubic planar bipartite graphs.

A systematic model study quantifying how conical intersection topography modulates photochemical reactions.

Despite their important role in photochemistry and expected presence in most polyatomic molecules, conical intersections have been thoroughly characterized in a comparatively small number of systems. Conical intersections can confer molecular photoreactivity or photostability, often with remarkable efficacy, due to their unique structure: at a conical intersection, the adiabatic potential energy surfaces of two or more electronic states are degenerate, enabling ultrafast decay from an excited state without radiative emission, known as nonadiabatic transfer. Furthermore, the precise conical intersection topography determines fundamental properties of photochemical processes, including excited-state decay rate, efficacy, and molecular products that are formed. However, these relationships have yet to be defined comprehensively. In this article, we use an adaptable computational model to investigate a variety of conical intersection topographies, simulate resulting nonadiabatic dynamics, and calculate key photochemical observables. We varied the vibrational mode frequencies to modify conical intersection topography systematically in four primary classes of conical intersections and quantified the resulting rate, total yield, and product yield of nonadiabatic decay. The results reveal that higher vibrational mode frequencies reduce nonadiabatic transfer, but increase the transfer rate and resulting photoproduct formation. These trends can inform progress toward experimental control of photochemical reactions or tuning of molecules' photochemical properties based on conical intersections and their topography.

An analogue of Dubrovin’s conjecture

We propose an analogue of Dubrovin's conjecture for the case where Fano manifolds have quantum connections of exponential type. It includes the case where the quantum cohomology rings are not necessarily semisimple. The conjecture is described as an isomorphism of two linear algebraic structures, which we call "mutation systems". Given such a Fano manifold $X$, one of the structures is given by the Stokes structure of the quantum connection of $X$, and the other is given by a semiorthogonal decomposition of the derived category of coherent sheaves on $X$. We also prove the conjecture for a class of smooth Fano complete intersections in a projective space.

On the Chern classes of singular complete intersections

We consider two classical extensions for singular varieties of the usual Chern classes of complex manifolds, namely the total Schwartz-MacPherson and Fulton-Johnson classes, $c^{SM}(X)$ and $c^{FJ}(X)$. Their difference (up to sign) is the total Milnor class ${\mathcal M}(X)$, a generalization of the Milnor number for varieties with arbitrary singular set. We get first Verdier-Riemann-Roch type formulae for the total classes $c^{SM}(X)$ and $c^{FJ}(X)$, and use these to prove a surprisingly simple formula for the total Milnor class when $X$ is defined by a finite number of local complete intersection $X_1,\cdot \ldots \cdot,X_r$ in a complex manifold, satisfying certain transversality conditions. As applications we obtain a Parusi\'{n}ski-Pragacz type formula and an Aluffi type formula for the Milnor class, and a description of the Milnor classes of $X$ in terms of the global L\^e classes of the $X_i$.