scholarly journals Fractional partitions and conjectures of Chern–Fu–Tang and Heim–Neuhauser

2021 ◽  
Vol 8 (21) ◽  
pp. 615-634
Author(s):  
Kathrin Bringmann ◽  
Ben Kane ◽  
Larry Rolen ◽  
Zack Tripp
Keyword(s):  
Partition Function ◽  
Future Study ◽  
Partition Functions ◽  
Colored Partitions ◽  
The Future ◽  
Error Terms ◽  
Partition Inequalities ◽  
User Friendly

Many papers have studied inequalities for partition functions. Recently, a number of papers have considered mixtures between additive and multiplicative behavior in such inequalities. In particular, Chern–Fu–Tang and Heim–Neuhauser gave conjectures on inequalities for coefficients of powers of the generating partition function. These conjectures were posed in the context of colored partitions and the Nekrasov–Okounkov formula. Here, we study the precise size of differences of products of two such coefficients. This allows us to prove the Chern–Fu–Tang conjecture and to show the Heim–Neuhauser conjecture in a certain range. The explicit error terms provided will also be useful in the future study of partition inequalities. These are laid out in a user-friendly way for the researcher in combinatorics interested in such analytic questions.

The Future Study of Public Opinion: A Symposium

1987 ◽  
Vol 51 (part 2: Supplement: 50th Anniversary Issue) ◽  
pp. S173
Author(s):  
Leo Bogart ◽  
James R. Beniger ◽  
Richard A. Brody ◽  
Irving Crespi ◽  
James A. Davis ◽  
...  
Keyword(s):  
Public Opinion ◽  
Future Study ◽  
The Future

scholarly journals Free partition functions and an averaged holographic duality

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Nima Afkhami-Jeddi ◽  
Henry Cohn ◽  
Thomas Hartman ◽  
Amirhossein Tajdini
Keyword(s):  
Partition Function ◽  
Spectral Gap ◽  
Central Charge ◽  
Three Dimensional ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Partition Functions ◽  
General Constraints ◽  
Dimensional Gravity ◽  
Holographic Duality

Abstract We study the torus partition functions of free bosonic CFTs in two dimensions. Integrating over Narain moduli defines an ensemble-averaged free CFT. We calculate the averaged partition function and show that it can be reinterpreted as a sum over topologies in three dimensions. This result leads us to conjecture that an averaged free CFT in two dimensions is holographically dual to an exotic theory of three-dimensional gravity with U(1)c×U(1)c symmetry and a composite boundary graviton. Additionally, for small central charge c, we obtain general constraints on the spectral gap of free CFTs using the spinning modular bootstrap, construct examples of Narain compactifications with a large gap, and find an analytic bootstrap functional corresponding to a single self-dual boson.

scholarly journals Gauge theories on compact toric manifolds

2021 ◽  
Vol 111 (3) ◽  
Author(s):  
Giulio Bonelli ◽  
Francesco Fucito ◽  
Jose Francisco Morales ◽  
Massimiliano Ronzani ◽  
Ekaterina Sysoeva ◽  
...  
Keyword(s):  
Partition Function ◽  
Gauge Theories ◽  
Blow Up ◽  
Gauge Coupling ◽  
Piecewise Constant Function ◽  
Partition Functions ◽  
Piecewise Constant ◽  
Toric Manifolds ◽  
Holomorphic Anomaly ◽  
The One

AbstractWe compute the $$\mathcal{N}=2$$ N = 2 supersymmetric partition function of a gauge theory on a four-dimensional compact toric manifold via equivariant localization. The result is given by a piecewise constant function of the Kähler form with jumps along the walls where the gauge symmetry gets enhanced. The partition function on such manifolds is written as a sum over the residues of a product of partition functions on $$\mathbb {C}^2$$ C 2 . The evaluation of these residues is greatly simplified by using an “abstruse duality” that relates the residues at the poles of the one-loop and instanton parts of the $$\mathbb {C}^2$$ C 2 partition function. As particular cases, our formulae compute the SU(2) and SU(3) equivariant Donaldson invariants of $$\mathbb {P}^2$$ P 2 and $$\mathbb {F}_n$$ F n and in the non-equivariant limit reproduce the results obtained via wall-crossing and blow up methods in the SU(2) case. Finally, we show that the U(1) self-dual connections induce an anomalous dependence on the gauge coupling, which turns out to satisfy a $$\mathcal {N}=2$$ N = 2 analog of the $$\mathcal {N}=4$$ N = 4 holomorphic anomaly equations.

scholarly journals Modular invariance in finite temperature Casimir effect

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Francesco Alessio ◽  
Glenn Barnich
Keyword(s):  
Partition Function ◽  
Chemical Potential ◽  
Casimir Effect ◽  
Temperature Inversion ◽  
Massless Scalar ◽  
Partition Functions ◽  
Parallel Plates ◽  
Modular Transformations ◽  
Real Analytic ◽  
Set Up

Abstract The temperature inversion symmetry of the partition function of the electromagnetic field in the set-up of the Casimir effect is extended to full modular transformations by turning on a purely imaginary chemical potential for adapted spin angular momentum. The extended partition function is expressed in terms of a real analytic Eisenstein series. These results become transparent after explicitly showing equivalence of the partition functions for Maxwell’s theory between perfectly conducting parallel plates and for a massless scalar with periodic boundary conditions.

scholarly journals Risk factors and mechanisms of stroke in young adults: The FUTURE study

2017 ◽  
Vol 38 (9) ◽  
pp. 1631-1641 ◽  
Author(s):  
Mayte E van Alebeek ◽  
Renate M Arntz ◽  
Merel S Ekker ◽  
Nathalie E Synhaeve ◽  
Noortje AMM Maaijwee ◽  
...  
Keyword(s):  
Risk Factors ◽  
Young Adults ◽  
Future Study ◽  
The Elderly ◽  
Classification Systems ◽  
Unknown Etiology ◽  
Stroke Patients ◽  
Young Stroke ◽  
Starting Point ◽  
The Future

Incidence of ischemic stroke and transient ischemic attack in young adults is rising. However, etiology remains unknown in 30–40% of these patients when current classification systems designed for the elderly are used. Our aim was to identify risk factors according to a pediatric approach, which might lead to both better identification of risk factors and provide a stepping stone for the understanding of disease mechanism, particularly in patients currently classified as “unknown etiology”. Risk factors of 656 young stroke patients (aged 18–50) of the FUTURE study were categorized according to the “International Pediatric Stroke Study” (IPSS), with stratification on gender, age and stroke of “unknown etiology”. Categorization of risk factors into ≥1 IPSS category was possible in 94% of young stroke patients. Chronic systemic conditions were more present in patients aged <35 compared to patients ≥35 (32.6% vs. 15.6%, p < 0.05). Among 226 patients classified as “stroke of unknown etiology” using TOAST, we found risk factors in 199 patients (88%) with the IPSS approach. We identified multiple risk factors linked to other mechanisms of stroke in the young than in the elderly . This can be a valuable starting point to develop an etiologic classification system specifically designed for young stroke patients.

Gigantomachy and Natural Philosophy

1979 ◽  
Vol 29 (1) ◽  
pp. 165-171 ◽  
Author(s):  
D. C. Innes
Keyword(s):  
Future Study ◽  
Natural Philosophy ◽  
The Future

Augustan poets refer curiously often to the possible composition of a Gigantomachy, as in Prop. 2.1 and 3.9, Ov. Am. 2.1.11 ff., Trist. 2.61 ff. and 331 ff., and the future study of natural philosophy, as in Verg. Georg. 2.475 ff. and Prop. 3.5.25 ff. These ambitions are rejected, abandoned, or firmly set in the future. I suggest that the function of both is closely similar since they provide traditionally sublime themes to contrast the poet's present ‘humbler’’ task.

ELIV 2021

2021 ◽  
Keyword(s):  
Automotive Industry ◽  
Digital Ecosystems ◽  
Start Up ◽  
The Future ◽  
User Friendly ◽  
Full Swing ◽  
Level 2 ◽  
The Way

Foreword Start-up future It has felt like Covid-19 had a stranglehold on us. But we haven‘t allowed ourselves to be defeated. On the contrary, we are taking advantage of the opportunities that arise as a result. Not only the long-overdue push towards digitalization, for example, but also the time gained by making fewer journeys. Those who show strength now and position themselves for the future will win. And that is exactly the reason why we have been preparing ELIV 2021 with such a lot of enthusiasm. As usual, we have prepared an up-to-date program with the familiar mixture of technically demanding and strategic papers and are sure that the ELIV platform will once again be a trendsetter for the automotive industry. The CASE megatrends (Connected, Autonomous, Shared, Electric) continue to disrupt the industry. In the Connect environment, there is still a struggle for user-friendly services and competition amongst digital ecosystems is in full swing. The entry of powerful central computers into electronic architectures poses major challenges for all parties involved. On the way from Level 2 to Levels 3, 4 and 5 all manufacturers are cur...

A COMPACT BOSON COUPLED TO TWO-DIMENSIONAL GRAVITY

1991 ◽  
Vol 06 (15) ◽  
pp. 2743-2754 ◽  
Author(s):  
NORISUKE SAKAI ◽  
YOSHIAKI TANII
Keyword(s):  
Field Theory ◽  
Partition Function ◽  
Quantum Gravity ◽  
Matrix Models ◽  
Riemann Surfaces ◽  
Partition Functions ◽  
Two Dimensional ◽  
Dimensional Gravity ◽  
The Continuum ◽  
Continuum Field

The radius dependence of partition functions is explicitly evaluated in the continuum field theory of a compactified boson, interacting with two-dimensional quantum gravity (noncritical string) on Riemann surfaces for the first few genera. The partition function for the torus is found to be a sum of terms proportional to R and 1/R. This is in agreement with the result of a discretized version (matrix models), but is quite different from the critical string. The supersymmetric case is also explicitly evaluated.

scholarly journals Algorithms for Estimating the Partition Function of Restricted Boltzmann Machines (Extended Abstract)

2020 ◽  
Author(s):  
Oswin Krause ◽  
Asja Fischer ◽  
Christian Igel
Keyword(s):  
Partition Function ◽  
Markov Random Fields ◽  
Probabilistic Models ◽  
Ratio Method ◽  
Parallel Tempering ◽  
Partition Functions ◽  
Path Sampling ◽  
Reference Distribution ◽  
Restricted Boltzmann Machines ◽  
Boltzmann Machines

Estimating the normalization constants (partition functions) of energy-based probabilistic models (Markov random fields) with a high accuracy is required for measuring performance, monitoring the training progress of adaptive models, and conducting likelihood ratio tests. We devised a unifying theoretical framework for algorithms for estimating the partition function, including Annealed Importance Sampling (AIS) and Bennett's Acceptance Ratio method (BAR). The unification reveals conceptual similarities of and differences between different approaches and suggests new algorithms. The framework is based on a generalized form of Crooks' equality, which links the expectation over a distribution of samples generated by a transition operator to the expectation over the distribution induced by the reversed operator. Different ways of sampling, such as parallel tempering and path sampling, are covered by the framework. We performed experiments in which we estimated the partition function of restricted Boltzmann machines (RBMs) and Ising models. We found that BAR using parallel tempering worked well with a small number of bridging distributions, while path sampling based AIS performed best with many bridging distributions. The normalization constant is measured w.r.t.~a reference distribution, and the choice of this distribution turned out to be very important in our experiments. Overall, BAR gave the best empirical results, outperforming AIS.

scholarly journals Automatic contraction of unstructured tensor networks

2020 ◽  
Vol 8 (1) ◽  
Author(s):  
Adam Jermyn
Keyword(s):  
Partition Function ◽  
Statistical Physics ◽  
Discrete Models ◽  
Correlation Structure ◽  
Central Problem ◽  
Partition Functions ◽  
Lattice Systems ◽  
Tensor Networks ◽  
Tensor Network

The evaluation of partition functions is a central problem in statistical physics. For lattice systems and other discrete models the partition function may be expressed as the contraction of a tensor network. Unfortunately computing such contractions is difficult, and many methods to make this tractable require periodic or otherwise structured networks. Here I present a new algorithm for contracting unstructured tensor networks. This method makes no assumptions about the structure of the network and performs well in both structured and unstructured cases so long as the correlation structure is local.

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