269 research outputs found
Impairments in probabilistic prediction and Bayesian learning can explain reduced neural semantic priming in schizophrenia
It has been proposed that abnormalities in probabilistic prediction and dynamic belief updating explain the multiple features of schizophrenia. Here, we used electroencephalography (EEG) to ask whether these abnormalities can account for the well-established reduction in semantic priming observed in schizophrenia under nonautomatic conditions. We isolated predictive contributions to the neural semantic priming effect by manipulating the prime’s predictive validity and minimizing retroactive semantic matching mechanisms. We additionally examined the link between prediction and learning using a Bayesian model that probed dynamic belief updating as participants adapted to the increase in predictive validity. We found that patients were less likely than healthy controls to use the prime to predictively facilitate semantic processing on the target, resulting in a reduced N400 effect. Moreover, the trial-by-trial output of our Bayesian computational model explained between-group differences in trial-by-trial N400 amplitudes as participants transitioned from conditions of lower to higher predictive validity. These findings suggest that, compared with healthy controls, people with schizophrenia are less able to mobilize predictive mechanisms to facilitate processing at the earliest stages of accessing the meanings of incoming words. This deficit may be linked to a failure to adapt to changes in the broader environment. This reciprocal relationship between impairments in probabilistic prediction and Bayesian learning/adaptation may drive a vicious cycle that maintains cognitive disturbances in schizophrenia
Topological Qubit Design and Leakage
We examine how best to design qubits for use in topological quantum
computation. These qubits are topological Hilbert spaces associated with small
groups of anyons. Op- erations are performed on these by exchanging the anyons.
One might argue that, in order to have as many simple single qubit operations
as possible, the number of anyons per group should be maximized. However, we
show that there is a maximal number of particles per qubit, namely 4, and more
generally a maximal number of particles for qudits of dimension d. We also look
at the possibility of having topological qubits for which one can perform
two-qubit gates without leakage into non-computational states. It turns out
that the requirement that all two-qubit gates are leakage free is very
restrictive and this property can only be realized for two-qubit systems
related to Ising-like anyon models, which do not allow for universal quantum
computation by braiding. Our results follow directly from the representation
theory of braid groups which means they are valid for all anyon models. We also
make some remarks on generalizations to other exchange groups.Comment: 13 pages, 3 figure
Spatiotemporal signatures of lexical–semantic prediction
Although there is broad agreement that top-down expectations can facilitate lexical-semantic processing, the mechanisms driving these effects are still unclear. In particular, while previous electroencephalography (EEG) research has demonstrated a reduction in the N400 response to words in a supportive context, it is often challenging to dissociate facilitation due to bottom-up spreading activation from facilitation due to top-down expectations. The goal of the current study was to specifically determine the cortical areas associated with facilitation due to top-down prediction, using magnetoencephalography (MEG) recordings supplemented by EEG and functional magnetic resonance imaging (fMRI) in a semantic priming paradigm. In order to modulate expectation processes while holding context constant, we manipulated the proportion of related pairs across 2 blocks (10 and 50% related). Event-related potential results demonstrated a larger N400 reduction when a related word was predicted, and MEG source localization of activity in this time-window (350-450 ms) localized the differential responses to left anterior temporal cortex. fMRI data from the same participants support the MEG localization, showing contextual facilitation in left anterior superior temporal gyrus for the high expectation block only. Together, these results provide strong evidence that facilitatory effects of lexical-semantic prediction on the electrophysiological response 350-450 ms postonset reflect modulation of activity in left anterior temporal cortex
Role of oxygen vacancy defect states in the n-type conduction of β-Ga[sub 2]O[sub 3]
Based on semiempirical quantum-chemical calculations, the electronic band structure of β-Ga2O3 is presented and the formation and properties of oxygen vacancies are analyzed. The equilibrium geometries and formation energies of neutral and doubly ionized vacancies were calculated. Using the calculated donor level positions of the vacancies, the high temperature n-type conduction is explained. The vacancy concentration is obtained by fitting to the experimental resistivity and electron mobility
Quantum algorithm for the Boolean hidden shift problem
The hidden shift problem is a natural place to look for new separations
between classical and quantum models of computation. One advantage of this
problem is its flexibility, since it can be defined for a whole range of
functions and a whole range of underlying groups. In a way, this distinguishes
it from the hidden subgroup problem where more stringent requirements about the
existence of a periodic subgroup have to be made. And yet, the hidden shift
problem proves to be rich enough to capture interesting features of problems of
algebraic, geometric, and combinatorial flavor. We present a quantum algorithm
to identify the hidden shift for any Boolean function. Using Fourier analysis
for Boolean functions we relate the time and query complexity of the algorithm
to an intrinsic property of the function, namely its minimum influence. We show
that for randomly chosen functions the time complexity of the algorithm is
polynomial. Based on this we show an average case exponential separation
between classical and quantum time complexity. A perhaps interesting aspect of
this work is that, while the extremal case of the Boolean hidden shift problem
over so-called bent functions can be reduced to a hidden subgroup problem over
an abelian group, the more general case studied here does not seem to allow
such a reduction.Comment: 10 pages, 1 figur
Contact numbers for congruent sphere packings in Euclidean 3-space
Continuing the investigations of Harborth (1974) and the author (2002) we
study the following two rather basic problems on sphere packings. Recall that
the contact graph of an arbitrary finite packing of unit balls (i.e., of an
arbitrary finite family of non-overlapping unit balls) in Euclidean 3-space is
the (simple) graph whose vertices correspond to the packing elements and whose
two vertices are connected by an edge if the corresponding two packing elements
touch each other. One of the most basic questions on contact graphs is to find
the maximum number of edges that a contact graph of a packing of n unit balls
can have in Euclidean 3-space. Our method for finding lower and upper estimates
for the largest contact numbers is a combination of analytic and combinatorial
ideas and it is also based on some recent results on sphere packings. Finally,
we are interested also in the following more special version of the above
problem. Namely, let us imagine that we are given a lattice unit sphere packing
with the center points forming the lattice L in Euclidean 3-space (and with
certain pairs of unit balls touching each other) and then let us generate
packings of n unit balls such that each and every center of the n unit balls is
chosen from L. Just as in the general case we are interested in finding good
estimates for the largest contact number of the packings of n unit balls
obtained in this way.Comment: 18 page
Exact expressions for correlations in the ground state of the dense O(1) loop model
Conjectures for analytical expressions for correlations in the dense O
loop model on semi infinite square lattices are given. We have obtained these
results for four types of boundary conditions. Periodic and reflecting boundary
conditions have been considered before. We give many new conjectures for these
two cases and review some of the existing results. We also consider boundaries
on which loops can end. We call such boundaries ''open''. We have obtained
expressions for correlations when both boundaries are open, and one is open and
the other one is reflecting. Also, we formulate a conjecture relating the
ground state of the model with open boundaries to Fully Packed Loop models on a
finite square grid. We also review earlier obtained results about this relation
for the three other types of boundary conditions. Finally, we construct a
mapping between the ground state of the dense O loop model and the XXZ
spin chain for the different types of boundary conditions.Comment: 25 pages, version accepted by JSTA
Quantum Commuting Circuits and Complexity of Ising Partition Functions
Instantaneous quantum polynomial-time (IQP) computation is a class of quantum
computation consisting only of commuting two-qubit gates and is not universal
in the sense of standard quantum computation. Nevertheless, it has been shown
that if there is a classical algorithm that can simulate IQP efficiently, the
polynomial hierarchy (PH) collapses at the third level, which is highly
implausible. However, the origin of the classical intractability is still less
understood. Here we establish a relationship between IQP and computational
complexity of the partition functions of Ising models. We apply the established
relationship in two opposite directions. One direction is to find subclasses of
IQP that are classically efficiently simulatable in the strong sense, by using
exact solvability of certain types of Ising models. Another direction is
applying quantum computational complexity of IQP to investigate (im)possibility
of efficient classical approximations of Ising models with imaginary coupling
constants. Specifically, we show that there is no fully polynomial randomized
approximation scheme (FPRAS) for Ising models with almost all imaginary
coupling constants even on a planar graph of a bounded degree, unless the PH
collapses at the third level. Furthermore, we also show a multiplicative
approximation of such a class of Ising partition functions is at least as hard
as a multiplicative approximation for the output distribution of an arbitrary
quantum circuit.Comment: 36 pages, 5 figure
Exact solution of the six-vertex model with domain wall boundary condition. Critical line between ferroelectric and disordered phases
This is a continuation of the papers [4] of Bleher and Fokin and [5] of
Bleher and Liechty, in which the large asymptotics is obtained for the
partition function of the six-vertex model with domain wall boundary
conditions in the disordered and ferroelectric phases, respectively. In the
present paper we obtain the large asymptotics of on the critical line
between these two phases.Comment: 22 pages, 6 figures, to appear in the Journal of Statistical Physic
The arctic curve of the domain-wall six-vertex model
The problem of the form of the `arctic' curve of the six-vertex model with
domain wall boundary conditions in its disordered regime is addressed. It is
well-known that in the scaling limit the model exhibits phase-separation, with
regions of order and disorder sharply separated by a smooth curve, called the
arctic curve. To find this curve, we study a multiple integral representation
for the emptiness formation probability, a correlation function devised to
detect spatial transition from order to disorder. We conjecture that the arctic
curve, for arbitrary choice of the vertex weights, can be characterized by the
condition of condensation of almost all roots of the corresponding saddle-point
equations at the same, known, value. In explicit calculations we restrict to
the disordered regime for which we have been able to compute the scaling limit
of certain generating function entering the saddle-point equations. The arctic
curve is obtained in parametric form and appears to be a non-algebraic curve in
general; it turns into an algebraic one in the so-called root-of-unity cases.
The arctic curve is also discussed in application to the limit shape of
-enumerated (with ) large alternating sign matrices. In
particular, as the limit shape tends to a nontrivial limiting curve,
given by a relatively simple equation.Comment: 39 pages, 2 figures; minor correction
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