Convex analysis for the log partition function
The Choquet integral of log convex functions
... for log-convex ...for log-convex ...and log-convex function that will be used ...monotone log- convex ...general log- convex function is ...
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The stringy instanton partition function
... This analysis would also be relevant in order to gain insights on a possible AGT counterpart [43] of our ...Nekrasov partition function we compute is interpreted in terms of type IIB superstring ...
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Approximating the Bethe partition function
... When belief propagation (BP) converges, it does so to a stationary point of the Bethe free energy F, and is often strikingly accurate. However, it may converge only to a local optimum or may not converge at all. An ...
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Applications of Combinatorial Analysis to the Calculation of the Partition Function of the Ising Model
... 2.4 More on the sign function The following lemma provides a combinatorial method for computing the sign of a word, with respect to any drawing of the cotree. Let w 1 and w 2 be c-reduced words. For i = 1, 2, let ...
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Refinements to Hadamard’s Inequality for Log Convex Functions
... positive log-convex function on [a,b], then f satisfies ...the log-convex function is convex which follows from the fact that “Every increasing convex ...
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On The Hadamard's Inequality for Log Convex Functions on the Coordinates
... coordinated log-convex function in Δ, then for all distinct x 1 , x 2 , x 3 ∈ a, b, such that x 1 < x 2 < x 3 and distinct y 1 , y 2 , y 3 ∈ c, d such that y 1 ...
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The Sugeno fuzzy integral of log convex functions
... every log-convex function is also ...logarithmically convex (log-convex) interference functions ...for log-convex functions using the classical Hadamard integral ...
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Computing the Partition Function for Cliques in a Graph
... the convex hull of any three vectors u i ,u j , u k since otherwise the angle between some two of these three vectors is at least ...the convex hull of the whole set of vectors u 1 , ...
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From convex to nonconvex: A loss function analysis for binary classification
... important convex loss functions, including hinge loss, square loss, modified square loss, exponential loss, logistic regression loss, as well as some non-convex loss functions, such as sigmoid loss, ϕ-loss, ...
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Convex-transitivity and function spaces
... −T (x) = y, so that X is in particular transitive. For recent results regarding somewhat economically produced homo- geneous spaces, see [19]. Acknowledgments This article is part of my PhD research supervised by H.-O. ...
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MacMahon's Partition Analysis VIII. Plane Partition Diamonds
... After considering some further questions about plane partitions on a square, MacMahon writes down the “crude form” for the general case, i.e., the expression for the full generating function for plane ...
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The partition function zeroes of quantum critical points
... lattice partition function of the quantum spin ...density function, which we identify as the entropy of the QMC ...FSS analysis of an AFM periodic mixed-spin model of the form 1 − 1 − 3/2 − ...
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Disciplined geometric programming is a subclass of log-log convex programming generated by a composition rule and a set of functions with known curvature under the log-log transformation
... a function formed from monomials using the operations addition, multiplication, positive power, and ...also convex under a logarithmic change of variable, after taking the log of the ...a ...
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The e-support function of an e-convex set and conjugacy for e-convex functions
... support function for e-convex sets and a conjugation scheme for e-convex ...support function of Convex Analysis is not appropriate for e-convex sets, since dif- ferent ...
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Approximating the Partition Function by Deleting and then Correcting for Model Edges
... After substituting into U β 0 , and some rearrangement: F 0 = U 0 − H 0 = U β − H β − log z = F β − log z as desired. To show this correspondence continues to hold for any tree-structured M 0 , we note ...
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The Fundamental Nature of the Log Loss Function
... loss function λ is continuous in the prediction p, so that the prediction set is a ...strictly convex (in particular, the prediction set has no straight segments) and that the points on the prediction set ...
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Analysis of Convex Functions
... certain convex functions on R n (their ...space. Convex functions are an important device for the study of extremal ...a convex function can have at most one minimum and no maxima is a notable ...
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Minimum convex partition of a constrained point set
... A convex partition with respect to a point set S is a planar subdivision whose vertices are the points of S, where the boundary of the unbounded outer face is the boundary of the convex hull of S, ...
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Bootstrapping the S5 partition function
... the partition function has poles at special values of the mass parameters due to the pinching mechanism of the integration contour, and taking the residues can be interpreted as RG flows to defect theories; ...
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Quantum Barnes Function as the Partition Function of the Resolved Conifold
... harmonic function is recovered from its boundary ...holomorphic function in the bulk the unit disk and the Donaldson-Thomas theory comes closest to being a bulk theory by giving its Taylor coefficients at ...
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