11,195 research outputs found
Logic and Topology for Knowledge, Knowability, and Belief - Extended Abstract
In recent work, Stalnaker proposes a logical framework in which belief is
realized as a weakened form of knowledge. Building on Stalnaker's core
insights, and using frameworks developed by Bjorndahl and Baltag et al., we
employ topological tools to refine and, we argue, improve on this analysis. The
structure of topological subset spaces allows for a natural distinction between
what is known and (roughly speaking) what is knowable; we argue that the
foundational axioms of Stalnaker's system rely intuitively on both of these
notions. More precisely, we argue that the plausibility of the principles
Stalnaker proposes relating knowledge and belief relies on a subtle
equivocation between an "evidence-in-hand" conception of knowledge and a weaker
"evidence-out-there" notion of what could come to be known. Our analysis leads
to a trimodal logic of knowledge, knowability, and belief interpreted in
topological subset spaces in which belief is definable in terms of knowledge
and knowability. We provide a sound and complete axiomatization for this logic
as well as its uni-modal belief fragment. We then consider weaker logics that
preserve suitable translations of Stalnaker's postulates, yet do not allow for
any reduction of belief. We propose novel topological semantics for these
irreducible notions of belief, generalizing our previous semantics, and provide
sound and complete axiomatizations for the corresponding logics.Comment: In Proceedings TARK 2017, arXiv:1707.08250. The full version of this
paper, including the longer proofs, is at arXiv:1612.0205
Backpropagation training in adaptive quantum networks
We introduce a robust, error-tolerant adaptive training algorithm for
generalized learning paradigms in high-dimensional superposed quantum networks,
or \emph{adaptive quantum networks}. The formalized procedure applies standard
backpropagation training across a coherent ensemble of discrete topological
configurations of individual neural networks, each of which is formally merged
into appropriate linear superposition within a predefined, decoherence-free
subspace. Quantum parallelism facilitates simultaneous training and revision of
the system within this coherent state space, resulting in accelerated
convergence to a stable network attractor under consequent iteration of the
implemented backpropagation algorithm. Parallel evolution of linear superposed
networks incorporating backpropagation training provides quantitative,
numerical indications for optimization of both single-neuron activation
functions and optimal reconfiguration of whole-network quantum structure.Comment: Talk presented at "Quantum Structures - 2008", Gdansk, Polan
Experimental observation of topological Fermi arcs in type-II Weyl semimetal MoTe2
Weyl semimetal is a new quantum state of matter [1-12] hosting the condensed
matter physics counterpart of relativisticWeyl fermion [13] originally
introduced in high energy physics. The Weyl semimetal realized in the TaAs
class features multiple Fermi arcs arising from topological surface states [10,
11, 14-16] and exhibits novel quantum phenomena, e.g., chiral anomaly induced
negative mag-netoresistance [17-19] and possibly emergent supersymmetry [20].
Recently it was proposed theoretically that a new type (type-II) of Weyl
fermion [21], which does not have counterpart in high energy physics due to the
breaking of Lorentz invariance, can emerge as topologically-protected touching
between electron and hole pockets. Here, we report direct spectroscopic
evidence of topological Fermi arcs in the predicted type-II Weyl semimetal
MoTe2 [22-24]. The topological surface states are confirmed by directly
observing the surface states using bulk-and surface-sensitive angle-resolved
photoemission spectroscopy (ARPES), and the quasi-particle interference (QPI)
pattern between the two putative Fermi arcs in scanning tunneling microscopy
(STM). Our work establishes MoTe2 as the first experimental realization of
type-II Weyl semimetal, and opens up new opportunities for probing novel
phenomena such as exotic magneto-transport [21] in type-II Weyl semimetals.Comment: submitted on 01/29/2016. Nature Physics, in press. Spectroscopic
evidence of the Fermi arcs from two complementary surface sensitive probes -
ARPES and STS. A comparison of the calculated band structure for T_d and 1T'
phase to identify the topological Fermi arcs in the T_d phase is also
included in the supplementary informatio
Geospatial Narratives and their Spatio-Temporal Dynamics: Commonsense Reasoning for High-level Analyses in Geographic Information Systems
The modelling, analysis, and visualisation of dynamic geospatial phenomena
has been identified as a key developmental challenge for next-generation
Geographic Information Systems (GIS). In this context, the envisaged
paradigmatic extensions to contemporary foundational GIS technology raises
fundamental questions concerning the ontological, formal representational, and
(analytical) computational methods that would underlie their spatial
information theoretic underpinnings.
We present the conceptual overview and architecture for the development of
high-level semantic and qualitative analytical capabilities for dynamic
geospatial domains. Building on formal methods in the areas of commonsense
reasoning, qualitative reasoning, spatial and temporal representation and
reasoning, reasoning about actions and change, and computational models of
narrative, we identify concrete theoretical and practical challenges that
accrue in the context of formal reasoning about `space, events, actions, and
change'. With this as a basis, and within the backdrop of an illustrated
scenario involving the spatio-temporal dynamics of urban narratives, we address
specific problems and solutions techniques chiefly involving `qualitative
abstraction', `data integration and spatial consistency', and `practical
geospatial abduction'. From a broad topical viewpoint, we propose that
next-generation dynamic GIS technology demands a transdisciplinary scientific
perspective that brings together Geography, Artificial Intelligence, and
Cognitive Science.
Keywords: artificial intelligence; cognitive systems; human-computer
interaction; geographic information systems; spatio-temporal dynamics;
computational models of narrative; geospatial analysis; geospatial modelling;
ontology; qualitative spatial modelling and reasoning; spatial assistance
systemsComment: ISPRS International Journal of Geo-Information (ISSN 2220-9964);
Special Issue on: Geospatial Monitoring and Modelling of Environmental
Change}. IJGI. Editor: Duccio Rocchini. (pre-print of article in press
Selective Control of Surface Spin Current in Topological Materials based on Pyrite-type OsX2 (X = Se, Te) Crystals
Topological materials host robust surface states, which could form the basis
for future electronic devices. As such states have spins that are locked to the
momentum, they are of particular interest for spintronic applications.
Understanding spin textures of the surface states of topologically nontrivial
materials, and being able to manipulate their polarization, is therefore
essential if they are to be utilized in future technologies. Here we use
first-principles calculations to show that pyrite-type crystals OsX2 (X= Se,
Te) are a class of topological material that can host surface states with spin
polarization that can be either in-plane or out-of-plane. We show that the
formation of low-energy states with symmetry-protected energy- and
direction-dependent spin textures on the (001) surface of these materials is a
consequence of a transformation from a topologically trivial to nontrivial
state, induced by spin orbit interactions. The unconventional spin textures of
these surface states feature an in-plane to out-of-plane spin polarization
transition in the momentum space protected by local symmetries. Moreover, the
surface spin direction and magnitude can be selectively filtered in specific
energy ranges. Our demonstration of a new class of topological material with
controllable spin textures provide a platform for experimentalists to detect
and exploit unconventional surface spin textures in future spin-based
nanoelectronic devices
Topological map of the body in post-stroke patients: lesional and hodological aspects
Objective: It has been repeatedly hypothesized that at least 3 distinct types of body representations do exist: body schema, a representation derived from multiple sensory and motor inputs; topological map of the body, a structural description of spatial relations among the body parts; and body semantics, a lexical-semantic representation. Although several studies have assessed neural correlates of the topological map of the body in healthy participants, a systematic investigation of neural underpinnings of the topological map of the body in brain-damaged patients is still lacking. Method: Here we investigated the neural substrates of topological map of the body in 23 brain-damaged patients, both from a topological and an hodological perspectives, using Voxel Lesion Symptom Mapping and atlas-based track-wise statistical analysis. Besides neuroimaging investigation, consisting of T1-weighted and FLAIR sequences, patients underwent the frontal body-evocation subtest (FBE) to assess the topological map of the body. Results: The present results reveal a large-scale brain network involved in the topological map of the body assessed with FBE, encompassing both regions of primary elaboration and multisensory associative areas, in the temporal, parietal, frontal, and insular cortices. Hodological analysis revealed significant association between processing of the body topological map and the disconnection of the frontomarginal tract. Conclusions: These findings suggest that the topological map of the body is built up basing on both external and internal information that comes from the body and are constantly updated and integrated. The theoretical and clinical relevance of these results is discussed
The Theory of the Interleaving Distance on Multidimensional Persistence Modules
In 2009, Chazal et al. introduced -interleavings of persistence
modules. -interleavings induce a pseudometric on (isomorphism
classes of) persistence modules, the interleaving distance. The definitions of
-interleavings and generalize readily to multidimensional
persistence modules. In this paper, we develop the theory of multidimensional
interleavings, with a view towards applications to topological data analysis.
We present four main results. First, we show that on 1-D persistence modules,
is equal to the bottleneck distance . This result, which first
appeared in an earlier preprint of this paper, has since appeared in several
other places, and is now known as the isometry theorem. Second, we present a
characterization of the -interleaving relation on multidimensional
persistence modules. This expresses transparently the sense in which two
-interleaved modules are algebraically similar. Third, using this
characterization, we show that when we define our persistence modules over a
prime field, satisfies a universality property. This universality result
is the central result of the paper. It says that satisfies a stability
property generalizing one which is known to satisfy, and that in
addition, if is any other pseudometric on multidimensional persistence
modules satisfying the same stability property, then . We also show
that a variant of this universality result holds for , over arbitrary
fields. Finally, we show that restricts to a metric on isomorphism
classes of finitely presented multidimensional persistence modules.Comment: Major revision; exposition improved throughout. To appear in
Foundations of Computational Mathematics. 36 page
- …