TY - JOUR
AB - The recently proposed diagrammatic expansion (DE) technique for the full Gutzwiller wave function (GWF) is applied to the Anderson lattice model. This approach allows for a systematic evaluation of the expectation values with full Gutzwiller wave function in finite-dimensional systems. It introduces results extending in an essential manner those obtained by means of the standard Gutzwiller approximation (GA), which is variationally exact only in infinite dimensions. Within the DE-GWF approach we discuss the principal paramagnetic properties and their relevance to heavy-fermion systems. We demonstrate the formation of an effective, narrow f band originating from atomic f-electron states and subsequently interpret this behavior as a direct itineracy of f electrons; it represents a combined effect of both the hybridization and the correlations induced by the Coulomb repulsive interaction. Such a feature is absent on the level of GA, which is equivalent to the zeroth order of our expansion. Formation of the hybridization- and electron-concentration-dependent narrow f band rationalizes the common assumption of such dispersion of f levels in the phenomenological modeling of the band structure of CeCoIn5. Moreover, it is shown that the emerging f-electron direct itineracy leads in a natural manner to three physically distinct regimes within a single model that are frequently discussed for 4f- or 5f-electron compounds as separate model situations. We identify these regimes as (i) the mixed-valence regime, (ii) Kondo/almost-Kondo insulating regime, and (iii) the Kondo-lattice limit when the f-electron occupancy is very close to the f-state half filling, ⟨nˆf⟩→1. The nonstandard features of the emerging correlated quantum liquid state are stressed.
AU - Wysokiński, Marcin
AU - Kaczmarczyk, Jan
AU - Spałek, Jozef
ID - 1696
IS - 12
JF - Physical Review B
TI - Gutzwiller wave function solution for Anderson lattice model: Emerging universal regimes of heavy quasiparticle states
VL - 92
ER -
TY - JOUR
AB - Motion tracking is a challenge the visual system has to solve by reading out the retinal population. It is still unclear how the information from different neurons can be combined together to estimate the position of an object. Here we recorded a large population of ganglion cells in a dense patch of salamander and guinea pig retinas while displaying a bar moving diffusively. We show that the bar’s position can be reconstructed from retinal activity with a precision in the hyperacuity regime using a linear decoder acting on 100+ cells. We then took advantage of this unprecedented precision to explore the spatial structure of the retina’s population code. The classical view would have suggested that the firing rates of the cells form a moving hill of activity tracking the bar’s position. Instead, we found that most ganglion cells in the salamander fired sparsely and idiosyncratically, so that their neural image did not track the bar. Furthermore, ganglion cell activity spanned an area much larger than predicted by their receptive fields, with cells coding for motion far in their surround. As a result, population redundancy was high, and we could find multiple, disjoint subsets of neurons that encoded the trajectory with high precision. This organization allows for diverse collections of ganglion cells to represent high-accuracy motion information in a form easily read out by downstream neural circuits.
AU - Marre, Olivier
AU - Botella Soler, Vicente
AU - Simmons, Kristina
AU - Mora, Thierry
AU - Tkacik, Gasper
AU - Berry, Michael
ID - 1697
IS - 7
JF - PLoS Computational Biology
TI - High accuracy decoding of dynamical motion from a large retinal population
VL - 11
ER -
TY - JOUR
AB - In mean-payoff games, the objective of the protagonist is to ensure that the limit average of an infinite sequence of numeric weights is nonnegative. In energy games, the objective is to ensure that the running sum of weights is always nonnegative. Multi-mean-payoff and multi-energy games replace individual weights by tuples, and the limit average (resp., running sum) of each coordinate must be (resp., remain) nonnegative. We prove finite-memory determinacy of multi-energy games and show inter-reducibility of multi-mean-payoff and multi-energy games for finite-memory strategies. We improve the computational complexity for solving both classes with finite-memory strategies: we prove coNP-completeness improving the previous known EXPSPACE bound. For memoryless strategies, we show that deciding the existence of a winning strategy for the protagonist is NP-complete. We present the first solution of multi-mean-payoff games with infinite-memory strategies: we show that mean-payoff-sup objectives can be decided in NP∩coNP, whereas mean-payoff-inf objectives are coNP-complete.
AU - Velner, Yaron
AU - Chatterjee, Krishnendu
AU - Doyen, Laurent
AU - Henzinger, Thomas A
AU - Rabinovich, Alexander
AU - Raskin, Jean
ID - 1698
IS - 4
JF - Information and Computation
TI - The complexity of multi-mean-payoff and multi-energy games
VL - 241
ER -
TY - JOUR
AB - By hybridization and backcrossing, alleles can surmount species boundaries and be incorporated into the genome of a related species. This introgression of genes is of particular evolutionary relevance if it involves the transfer of adaptations between populations. However, any beneficial allele will typically be associated with other alien alleles that are often deleterious and hamper the introgression process. In order to describe the introgression of an adaptive allele, we set up a stochastic model with an explicit genetic makeup of linked and unlinked deleterious alleles. Based on the theory of reducible multitype branching processes, we derive a recursive expression for the establishment probability of the beneficial allele after a single hybridization event. We furthermore study the probability that slightly deleterious alleles hitchhike to fixation. The key to the analysis is a split of the process into a stochastic phase in which the advantageous alleles establishes and a deterministic phase in which it sweeps to fixation. We thereafter apply the theory to a set of biologically relevant scenarios such as introgression in the presence of many unlinked or few closely linked deleterious alleles. A comparison to computer simulations shows that the approximations work well over a large parameter range.
AU - Uecker, Hildegard
AU - Setter, Derek
AU - Hermisson, Joachim
ID - 1699
IS - 7
JF - Journal of Mathematical Biology
TI - Adaptive gene introgression after secondary contact
VL - 70
ER -
TY - JOUR
AB - We use the dual boson approach to reveal the phase diagram of the Fermi-Hubbard model with long-range dipole-dipole interactions. By using a large-scale finite-temperature calculation on a 64×64 square lattice we demonstrate the existence of a novel phase, possessing an "ultralong-range" order. The fingerprint of this phase - the density correlation function - features a nontrivial behavior on a scale of tens of lattice sites. We study the properties and the stability of the ultralong-range-ordered phase, and show that it is accessible in modern experiments with ultracold polar molecules and magnetic atoms.
AU - Van Loon, Erik
AU - Katsnelson, Mikhail
AU - Lemeshko, Mikhail
ID - 1700
IS - 8
JF - Physical Review B
TI - Ultralong-range order in the Fermi-Hubbard model with long-range interactions
VL - 92
ER -
TY - JOUR
AB - The activity of a neural network is defined by patterns of spiking and silence from the individual neurons. Because spikes are (relatively) sparse, patterns of activity with increasing numbers of spikes are less probable, but, with more spikes, the number of possible patterns increases. This tradeoff between probability and numerosity is mathematically equivalent to the relationship between entropy and energy in statistical physics. We construct this relationship for populations of up to N = 160 neurons in a small patch of the vertebrate retina, using a combination of direct and model-based analyses of experiments on the response of this network to naturalistic movies. We see signs of a thermodynamic limit, where the entropy per neuron approaches a smooth function of the energy per neuron as N increases. The form of this function corresponds to the distribution of activity being poised near an unusual kind of critical point. We suggest further tests of criticality, and give a brief discussion of its functional significance.
AU - Tkacik, Gasper
AU - Mora, Thierry
AU - Marre, Olivier
AU - Amodei, Dario
AU - Palmer, Stephanie
AU - Berry Ii, Michael
AU - Bialek, William
ID - 1701
IS - 37
JF - PNAS
TI - Thermodynamics and signatures of criticality in a network of neurons
VL - 112
ER -
TY - JOUR
AB - Vegetation clearing and land-use change have depleted many natural plant communities to the point where restoration is required. A major impediment to the success of rebuilding complex vegetation communities is having regular access to sufficient quantities of high-quality seed. Seed-production areas (SPAs) can help generate this seed, but these must be underpinned by a broad genetic base to maximise the evolutionary potential of restored populations. However, genetic bottlenecks can occur at the collection, establishment and production stages in SPAs, requiring genetic evaluation. This is especially relevant for species that may take many years before a return on SPA investment is realised. Two recently established yellow box (Eucalyptus melliodora A.Cunn. ex Schauer, Myrtaceae) SPAs were evaluated to determine whether genetic bottlenecks had occurred between seed collection and SPA establishment. No evidence was found to suggest that a significant loss of genetic diversity had occurred at this stage, although there was a significant difference in diversity between the two SPAs. Complex population genetic structure was also observed in the seed used to source the SPAs, with up to eight groups identified. Plant survival in the SPAs was influenced by seed collection location but not by SPA location and was not associated with genetic diversity. There were also no associations between genetic diversity and plant growth. These data highlighted the importance of chance events when establishing SPAs and indicated that the two yellow box SPAs are likely to provide genetically diverse seed sources for future restoration projects, especially by pooling seed from both SPAs.
AU - Broadhurst, Linda
AU - Fifield, Graham
AU - Vanzella, Bindi
AU - Pickup, Melinda
ID - 1703
IS - 5
JF - Australian Journal of Botany
TI - An evaluation of the genetic structure of seed sources and the maintenance of genetic diversity during establishment of two yellow box (Eucalyptus melliodora) seed-production areas
VL - 63
ER -
TY - JOUR
AB - Given a convex function (Formula presented.) and two hermitian matrices A and B, Lewin and Sabin study in (Lett Math Phys 104:691–705, 2014) the relative entropy defined by (Formula presented.). Among other things, they prove that the so-defined quantity is monotone if and only if (Formula presented.) is operator monotone. The monotonicity is then used to properly define (Formula presented.) for bounded self-adjoint operators acting on an infinite-dimensional Hilbert space by a limiting procedure. More precisely, for an increasing sequence of finite-dimensional projections (Formula presented.) with (Formula presented.) strongly, the limit (Formula presented.) is shown to exist and to be independent of the sequence of projections (Formula presented.). The question whether this sequence converges to its "obvious" limit, namely (Formula presented.), has been left open. We answer this question in principle affirmatively and show that (Formula presented.). If the operators A and B are regular enough, that is (A − B), (Formula presented.) and (Formula presented.) are trace-class, the identity (Formula presented.) holds.
AU - Deuchert, Andreas
AU - Hainzl, Christian
AU - Seiringer, Robert
ID - 1704
IS - 10
JF - Letters in Mathematical Physics
TI - Note on a family of monotone quantum relative entropies
VL - 105
ER -
TY - CONF
AB - We consider a problem of learning kernels for use in SVM classification in the multi-task and lifelong scenarios and provide generalization bounds on the error of a large margin classifier. Our results show that, under mild conditions on the family of kernels used for learning, solving several related tasks simultaneously is beneficial over single task learning. In particular, as the number of observed tasks grows, assuming that in the considered family of kernels there exists one that yields low approximation error on all tasks, the overhead associated with learning such a kernel vanishes and the complexity converges to that of learning when this good kernel is given to the learner.
AU - Pentina, Anastasia
AU - Ben David, Shai
ID - 1706
TI - Multi-task and lifelong learning of kernels
VL - 9355
ER -
TY - JOUR
AB - The competition for resources among cells, individuals or species is a fundamental characteristic of evolution. Biological all-pay auctions have been used to model situations where multiple individuals compete for a single resource. However, in many situations multiple resources with various values exist and single reward auctions are not applicable. We generalize the model to multiple rewards and study the evolution of strategies. In biological all-pay auctions the bid of an individual corresponds to its strategy and is equivalent to its payment in the auction. The decreasingly ordered rewards are distributed according to the decreasingly ordered bids of the participating individuals. The reproductive success of an individual is proportional to its fitness given by the sum of the rewards won minus its payments. Hence, successful bidding strategies spread in the population. We find that the results for the multiple reward case are very different from the single reward case. While the mixed strategy equilibrium in the single reward case with more than two players consists of mostly low-bidding individuals, we show that the equilibrium can convert to many high-bidding individuals and a few low-bidding individuals in the multiple reward case. Some reward values lead to a specialization among the individuals where one subpopulation competes for the rewards and the other subpopulation largely avoids costly competitions. Whether the mixed strategy equilibrium is an evolutionarily stable strategy (ESS) depends on the specific values of the rewards.
AU - Reiter, Johannes
AU - Kanodia, Ayush
AU - Gupta, Raghav
AU - Nowak, Martin
AU - Chatterjee, Krishnendu
ID - 1709
IS - 1812
JF - Proceedings of the Royal Society of London Series B Biological Sciences
TI - Biological auctions with multiple rewards
VL - 282
ER -
TY - JOUR
AB - We consider the hollow on the half-plane {(x, y) : y ≤ 0} ⊂ ℝ2 defined by a function u : (-1, 1) → ℝ, u(x) < 0, and a vertical flow of point particles incident on the hollow. It is assumed that u satisfies the so-called single impact condition (SIC): each incident particle is elastically reflected by graph(u) and goes away without hitting the graph of u anymore. We solve the problem: find the function u minimizing the force of resistance created by the flow. We show that the graph of the minimizer is formed by two arcs of parabolas symmetric to each other with respect to the y-axis. Assuming that the resistance of u ≡ 0 equals 1, we show that the minimal resistance equals π/2 - 2arctan(1/2) ≈ 0.6435. This result completes the previously obtained result [SIAM J. Math. Anal., 46 (2014), pp. 2730-2742] stating in particular that the minimal resistance of a hollow in higher dimensions equals 0.5. We additionally consider a similar problem of minimal resistance, where the hollow in the half-space {(x1,...,xd,y) : y ≤ 0} ⊂ ℝd+1 is defined by a radial function U satisfying the SIC, U(x) = u(|x|), with x = (x1,...,xd), u(ξ) < 0 for 0 ≤ ξ < 1, and u(ξ) = 0 for ξ ≥ 1, and the flow is parallel to the y-axis. The minimal resistance is greater than 0.5 (and coincides with 0.6435 when d = 1) and converges to 0.5 as d → ∞.
AU - Akopyan, Arseniy
AU - Plakhov, Alexander
ID - 1710
IS - 4
JF - Society for Industrial and Applied Mathematics
TI - Minimal resistance of curves under the single impact assumption
VL - 47
ER -
TY - JOUR
AB - The majority of immune cells in Drosophila melanogaster are plasmatocytes; they carry out similar functions to vertebrate macrophages, influencing development as well as protecting against infection and cancer. Plasmatocytes, sometimes referred to with the broader term of hemocytes, migrate widely during embryonic development and cycle in the larvae between sessile and circulating positions. Here we discuss the similarities of plasmatocyte developmental migration and its functions to that of vertebrate macrophages, considering the recent controversy regarding the functions of Drosophila PDGF/VEGF related ligands. We also examine recent findings on the significance of adhesion for plasmatocyte migration in the embryo, as well as proliferation, trans-differentiation, and tumor responses in the larva. We spotlight parallels throughout to vertebrate immune responses.
AU - Ratheesh, Aparna
AU - Belyaeva, Vera
AU - Siekhaus, Daria E
ID - 1712
IS - 10
JF - Current Opinion in Cell Biology
TI - Drosophila immune cell migration and adhesion during embryonic development and larval immune responses
VL - 36
ER -
TY - CONF
AB - We present a flexible framework for the automated competitive analysis of on-line scheduling algorithms for firm-deadline real-time tasks based on multi-objective graphs: Given a task set and an on-line scheduling algorithm specified as a labeled transition system, along with some optional safety, liveness, and/or limit-average constraints for the adversary, we automatically compute the competitive ratio of the algorithm w.r.t. A clairvoyant scheduler. We demonstrate the flexibility and power of our approach by comparing the competitive ratio of several on-line algorithms, including Dover, that have been proposed in the past, for various task sets. Our experimental results reveal that none of these algorithms is universally optimal, in the sense that there are task sets where other schedulers provide better performance. Our framework is hence a very useful design tool for selecting optimal algorithms for a given application.
AU - Chatterjee, Krishnendu
AU - Pavlogiannis, Andreas
AU - Kößler, Alexander
AU - Schmid, Ulrich
ID - 1714
IS - January
T2 - Real-Time Systems Symposium
TI - A framework for automated competitive analysis of on-line scheduling of firm-deadline tasks
VL - 2015
ER -
TY - JOUR
AB - How much cutting is needed to simplify the topology of a surface? We provide bounds for several instances of this question, for the minimum length of topologically non-trivial closed curves, pants decompositions, and cut graphs with a given combinatorial map in triangulated combinatorial surfaces (or their dual cross-metric counterpart). Our work builds upon Riemannian systolic inequalities, which bound the minimum length of non-trivial closed curves in terms of the genus and the area of the surface. We first describe a systematic way to translate Riemannian systolic inequalities to a discrete setting, and vice-versa. This implies a conjecture by Przytycka and Przytycki (Graph structure theory. Contemporary Mathematics, vol. 147, 1993), a number of new systolic inequalities in the discrete setting, and the fact that a theorem of Hutchinson on the edge-width of triangulated surfaces and Gromov’s systolic inequality for surfaces are essentially equivalent. We also discuss how these proofs generalize to higher dimensions. Then we focus on topological decompositions of surfaces. Relying on ideas of Buser, we prove the existence of pants decompositions of length O(g^(3/2)n^(1/2)) for any triangulated combinatorial surface of genus g with n triangles, and describe an O(gn)-time algorithm to compute such a decomposition. Finally, we consider the problem of embedding a cut graph (or more generally a cellular graph) with a given combinatorial map on a given surface. Using random triangulations, we prove (essentially) that, for any choice of a combinatorial map, there are some surfaces on which any cellular embedding with that combinatorial map has length superlinear in the number of triangles of the triangulated combinatorial surface. There is also a similar result for graphs embedded on polyhedral triangulations.
AU - Colin De Verdière, Éric
AU - Hubard, Alfredo
AU - De Mesmay, Arnaud N
ID - 1730
IS - 3
JF - Discrete & Computational Geometry
TI - Discrete systolic inequalities and decompositions of triangulated surfaces
VL - 53
ER -
TY - JOUR
AB - We consider two-player zero-sum games on graphs. These games can be classified on the basis of the information of the players and on the mode of interaction between them. On the basis of information the classification is as follows: (a) partial-observation (both players have partial view of the game); (b) one-sided complete-observation (one player has complete observation); and (c) complete-observation (both players have complete view of the game). On the basis of mode of interaction we have the following classification: (a) concurrent (both players interact simultaneously); and (b) turn-based (both players interact in turn). The two sources of randomness in these games are randomness in transition function and randomness in strategies. In general, randomized strategies are more powerful than deterministic strategies, and randomness in transitions gives more general classes of games. In this work we present a complete characterization for the classes of games where randomness is not helpful in: (a) the transition function probabilistic transition can be simulated by deterministic transition); and (b) strategies (pure strategies are as powerful as randomized strategies). As consequence of our characterization we obtain new undecidability results for these games.
AU - Chatterjee, Krishnendu
AU - Doyen, Laurent
AU - Gimbert, Hugo
AU - Henzinger, Thomas A
ID - 1731
IS - 12
JF - Information and Computation
TI - Randomness for free
VL - 245
ER -
TY - CONF
AB - We consider partially observable Markov decision processes (POMDPs), that are a standard framework for robotics applications to model uncertainties present in the real world, with temporal logic specifications. All temporal logic specifications in linear-time temporal logic (LTL) can be expressed as parity objectives. We study the qualitative analysis problem for POMDPs with parity objectives that asks whether there is a controller (policy) to ensure that the objective holds with probability 1 (almost-surely). While the qualitative analysis of POMDPs with parity objectives is undecidable, recent results show that when restricted to finite-memory policies the problem is EXPTIME-complete. While the problem is intractable in theory, we present a practical approach to solve the qualitative analysis problem. We designed several heuristics to deal with the exponential complexity, and have used our implementation on a number of well-known POMDP examples for robotics applications. Our results provide the first practical approach to solve the qualitative analysis of robot motion planning with LTL properties in the presence of uncertainty.
AU - Chatterjee, Krishnendu
AU - Chmelik, Martin
AU - Gupta, Raghav
AU - Kanodia, Ayush
ID - 1732
TI - Qualitative analysis of POMDPs with temporal logic specifications for robotics applications
ER -
TY - JOUR
AB - Facial appearance capture is now firmly established within academic research and used extensively across various application domains, perhaps most prominently in the entertainment industry through the design of virtual characters in video games and films. While significant progress has occurred over the last two decades, no single survey currently exists that discusses the similarities, differences, and practical considerations of the available appearance capture techniques as applied to human faces. A central difficulty of facial appearance capture is the way light interacts with skin-which has a complex multi-layered structure-and the interactions that occur below the skin surface can, by definition, only be observed indirectly. In this report, we distinguish between two broad strategies for dealing with this complexity. "Image-based methods" try to exhaustively capture the exact face appearance under different lighting and viewing conditions, and then render the face through weighted image combinations. "Parametric methods" instead fit the captured reflectance data to some parametric appearance model used during rendering, allowing for a more lightweight and flexible representation but at the cost of potentially increased rendering complexity or inexact reproduction. The goal of this report is to provide an overview that can guide practitioners and researchers in assessing the tradeoffs between current approaches and identifying directions for future advances in facial appearance capture.
AU - Klehm, Oliver
AU - Rousselle, Fabrice
AU - Papas, Marios
AU - Bradley, Derek
AU - Hery, Christophe
AU - Bickel, Bernd
AU - Jarosz, Wojciech
AU - Beeler, Thabo
ID - 1734
IS - 2
JF - Computer Graphics Forum
TI - Recent advances in facial appearance capture
VL - 34
ER -
TY - JOUR
AB - This work presents a method for efficiently simplifying the pressure projection step in a liquid simulation. We first devise a straightforward dimension reduction technique that dramatically reduces the cost of solving the pressure projection. Next, we introduce a novel change of basis that satisfies free-surface boundary conditions exactly, regardless of the accuracy of the pressure solve. When combined, these ideas greatly reduce the computational complexity of the pressure solve without compromising free surface boundary conditions at the highest level of detail. Our techniques are easy to parallelize, and they effectively eliminate the computational bottleneck for large liquid simulations.
AU - Ando, Ryoichi
AU - Thürey, Nils
AU - Wojtan, Christopher J
ID - 1735
IS - 2
JF - Computer Graphics Forum
TI - A dimension-reduced pressure solver for liquid simulations
VL - 34
ER -
TY - JOUR
AB - Intellectual disability (ID) has an estimated prevalence of 2-3%. Due to its extreme heterogeneity, the genetic basis of ID remains elusive in many cases. Recently, whole exome sequencing (WES) studies revealed that a large proportion of sporadic cases are caused by de novo gene variants. To identify further genes involved in ID, we performed WES in 250 patients with unexplained ID and their unaffected parents and included exomes of 51 previously sequenced child-parents trios in the analysis. Exome analysis revealed de novo intragenic variants in SET domain-containing 5 (SETD5) in two patients. One patient carried a nonsense variant, and the other an 81 bp deletion located across a splice-donor site. Chromosomal microarray diagnostics further identified four de novo non-recurrent microdeletions encompassing SETD5. CRISPR/Cas9 mutation modelling of the two intragenic variants demonstrated nonsense-mediated decay of the resulting transcripts, pointing to a loss-of-function (LoF) and haploinsufficiency as the common disease-causing mechanism of intragenic SETD5 sequence variants and SETD5-containing microdeletions. In silico domain prediction of SETD5, a predicted SET domain-containing histone methyltransferase (HMT), substantiated the presence of a SET domain and identified a novel putative PHD domain, strengthening a functional link to well-known histone-modifying ID genes. All six patients presented with ID and certain facial dysmorphisms, suggesting that SETD5 sequence variants contribute substantially to the microdeletion 3p25.3 phenotype. The present report of two SETD5 LoF variants in 301 patients demonstrates a prevalence of 0.7% and thus SETD5 variants as a relatively frequent cause of ID.
AU - Kuechler, Alma
AU - Zink, Alexander
AU - Wieland, Thomas
AU - Lüdecke, Hermann
AU - Cremer, Kirsten
AU - Salviati, Leonardo
AU - Magini, Pamela
AU - Najafi, Kimia
AU - Zweier, Christiane
AU - Czeschik, Johanna
AU - Aretz, Stefan
AU - Endele, Sabine
AU - Tamburrino, Federica
AU - Pinato, Claudia
AU - Clementi, Maurizio
AU - Gundlach, Jasmin
AU - Maylahn, Carina
AU - Mazzanti, Laura
AU - Wohlleber, Eva
AU - Schwarzmayr, Thomas
AU - Kariminejad, Roxana
AU - Schlessinger, Avner
AU - Wieczorek, Dagmar
AU - Strom, Tim
AU - Novarino, Gaia
AU - Engels, Hartmut
ID - 1789
IS - 6
JF - European Journal of Human Genetics
TI - Loss-of-function variants of SETD5 cause intellectual disability and the core phenotype of microdeletion 3p25.3 syndrome
VL - 23
ER -
TY - JOUR
AB - Motivated by recent ideas of Harman (Unif. Distrib. Theory, 2010) we develop a new concept of variation of multivariate functions on a compact Hausdorff space with respect to a collection D of subsets. We prove a general version of the Koksma-Hlawka theorem that holds for this notion of variation and discrepancy with respect to D. As special cases, we obtain Koksma-Hlawka inequalities for classical notions, such as extreme or isotropic discrepancy. For extreme discrepancy, our result coincides with the usual Koksma-Hlawka theorem. We show that the space of functions of bounded D-variation contains important discontinuous functions and is closed under natural algebraic operations. Finally, we illustrate the results on concrete integration problems from integral geometry and stereology.
AU - Pausinger, Florian
AU - Svane, Anne
ID - 1792
IS - 6
JF - Journal of Complexity
TI - A Koksma-Hlawka inequality for general discrepancy systems
VL - 31
ER -