TY - JOUR
AB - Châtelet surfaces provide a rich source of geometrically rational surfaces that do not always satisfy the Hasse principle. Restricting attention to a special class of Châtelet surfaces, we investigate the frequency that such counter-examples arise over the rational numbers.
AU - de la Bretèche, Régis
AU - Timothy Browning
ID - 250
IS - 4
JF - Proceedings of the London Mathematical Society
TI - Density of Châtelet surfaces failing the Hasse principle
VL - 108
ER -
TY - CONF
AB - Traditional formal methods are based on a Boolean satisfaction notion: a reactive system satisfies, or not, a given specification. We generalize formal methods to also address the quality of systems. As an adequate specification formalism we introduce the linear temporal logic LTL[F]. The satisfaction value of an LTL[F] formula is a number between 0 and 1, describing the quality of the satisfaction. The logic generalizes traditional LTL by augmenting it with a (parameterized) set F of arbitrary functions over the interval [0,1]. For example, F may contain the maximum or minimum between the satisfaction values of subformulas, their product, and their average. The classical decision problems in formal methods, such as satisfiability, model checking, and synthesis, are generalized to search and optimization problems in the quantitative setting. For example, model checking asks for the quality in which a specification is satisfied, and synthesis returns a system satisfying the specification with the highest quality. Reasoning about quality gives rise to other natural questions, like the distance between specifications. We formalize these basic questions and study them for LTL[F]. By extending the automata-theoretic approach for LTL to a setting that takes quality into an account, we are able to solve the above problems and show that reasoning about LTL[F] has roughly the same complexity as reasoning about traditional LTL.
AU - Almagor, Shaull
AU - Boker, Udi
AU - Kupferman, Orna
ID - 2517
IS - Part 2
TI - Formalizing and reasoning about quality
VL - 7966
ER -
TY - CONF
AB - A class of valued constraint satisfaction problems (VCSPs) is characterised by a valued constraint language, a fixed set of cost functions on a finite domain. An instance of the problem is specified by a sum of cost functions from the language with the goal to minimise the sum. We study which classes of finite-valued languages can be solved exactly by the basic linear programming relaxation (BLP). Thapper and Živný showed [20] that if BLP solves the language then the language admits a binary commutative fractional polymorphism. We prove that the converse is also true. This leads to a necessary and a sufficient condition which can be checked in polynomial time for a given language. In contrast, the previous necessary and sufficient condition due to [20] involved infinitely many inequalities. More recently, Thapper and Živný [21] showed (using, in particular, a technique introduced in this paper) that core languages that do not satisfy our condition are NP-hard. Taken together, these results imply that a finite-valued language can either be solved using Linear Programming or is NP-hard.
AU - Kolmogorov, Vladimir
ID - 2518
IS - 1
TI - The power of linear programming for finite-valued CSPs: A constructive characterization
VL - 7965
ER -
TY - CONF
AB - We propose a probabilistic model to infer supervised latent variables in
the Hamming space from observed data. Our model allows simultaneous
inference of the number of binary latent variables, and their values. The
latent variables preserve neighbourhood structure of the data in a sense
that objects in the same semantic concept have similar latent values, and
objects in different concepts have dissimilar latent values. We formulate
the supervised infinite latent variable problem based on an intuitive
principle of pulling objects together if they are of the same type, and
pushing them apart if they are not. We then combine this principle with a
flexible Indian Buffet Process prior on the latent variables. We show that
the inferred supervised latent variables can be directly used to perform a
nearest neighbour search for the purpose of retrieval. We introduce a new
application of dynamically extending hash codes, and show how to
effectively couple the structure of the hash codes with continuously
growing structure of the neighbourhood preserving infinite latent feature
space.
AU - Quadrianto, Novi
AU - Sharmanska, Viktoriia
AU - Knowles, David
AU - Ghahramani, Zoubin
ID - 2520
SN - 9780974903996
T2 - Proceedings of the 29th conference uncertainty in Artificial Intelligence
TI - The supervised IBP: Neighbourhood preserving infinite latent feature models
ER -
TY - JOUR
AB - Understanding the relative importance of heterosis and outbreeding depression over multiple generations is a key question in evolutionary biology and is essential for identifying appropriate genetic sources for population and ecosystem restoration. Here we use 2455 experimental crosses between 12 population pairs of the rare perennial plant Rutidosis leptorrhynchoides (Asteraceae) to investigate the multi-generational (F1, F2, F3) fitness outcomes of inter-population hybridization. We detected no evidence of outbreeding depression, with inter-population hybrids and backcrosses showing either similar fitness or significant heterosis for fitness components across the three generations. Variation in heterosis among population pairs was best explained by characteristics of the foreign source or home population, and was greatest when the source population was large, with high genetic diversity and low inbreeding, and the home population was small and inbred. Our results indicate that the primary consideration for maximizing progeny fitness following population augmentation or restoration is the use of seed from large, genetically diverse populations.
AU - Pickup, Melinda
AU - Field, David
AU - Rowell, David
AU - Young, Andrew
ID - 450
IS - 1750
JF - Proceedings of the Royal Society of London Series B Biological Sciences
TI - Source population characteristics affect heterosis following genetic rescue of fragmented plant populations
VL - 280
ER -