scholarly journals Complex curve of the two-matrix model and its tau-function

2003 ◽  
Vol 36 (12) ◽  
pp. 3107-3136 ◽  
Author(s):  
Vladimir A Kazakov ◽  
Andrei Marshakov
Keyword(s):  
Matrix Model ◽  
Tau Function ◽  
Complex Curve

scholarly journals Topological recursion with hard edges

2019 ◽  
Vol 30 (03) ◽  
pp. 1950014
Author(s):  
Leonid Chekhov ◽  
Paul Norbury
Keyword(s):  
Matrix Model ◽  
Spectral Curve ◽  
Partition Functions ◽  
Tau Function ◽  
Spectral Curves ◽  
Topological Recursion ◽  
The Matrix ◽  
Type Decomposition

We prove a Givental type decomposition for partition functions that arise out of topological recursion applied to spectral curves. Copies of the Konstevich–Witten KdV tau function arise out of regular spectral curves and copies of the Brezin–Gross–Witten KdV tau function arise out of irregular spectral curves. We present the example of this decomposition for the matrix model with two hard edges and spectral curve [Formula: see text].

Toward a relational matrix model of avatar-mediated interactions.

2019 ◽  
Vol 8 (3) ◽  
pp. 287-295 ◽  
Author(s):  
Jaime Banks ◽  
Caleb T. Carr
Keyword(s):  
Matrix Model

Developing the basis of the matrix model of the regional innovation subsystem

2020 ◽  
Vol 18 (11) ◽  
pp. 2183-2204
Author(s):  
E.I. Moskvitina
Keyword(s):  
Russian Federation ◽  
Matrix Model ◽  
Federal District ◽  
Assessment Method ◽  
Expert Assessment ◽  
Regional Innovation ◽  
Regional Strategies ◽  
Analysis And Synthesis ◽  
The Matrix ◽  
The Russian Federation

Subject. This article deals with the issues related to the formation and implementation of the innovation capacity of the Russian Federation subjects. Objectives. The article aims to develop the organizational and methodological foundations for the formation of a model of the regional innovation subsystem. Methods. For the study, I used the methods of analysis and synthesis, economics and statistics analysis, and the expert assessment method. Results. The article presents a developed basis of the regional innovation subsystem matrix model. It helps determine the relationship between the subjects and the parameters of the regional innovation subsystem. To evaluate the indicators characterizing the selected parameters, the Volga Federal District regions are considered as a case study. The article defines the process of reconciliation of interests between the subjects of regional innovation. Conclusions. The results obtained can be used by regional executive bodies when developing regional strategies for the socio-economic advancement of the Russian Federation subjects.

5-Benzylidene-4-Oxazolidinones are Synergistic with Antibiotics for the Treatment of Staphylococcus Aureus Biofilms

2019 ◽  
Author(s):  
Bram Frohock ◽  
Jessica M. Gilbertie ◽  
Jennifer C. Daiker ◽  
Lauren V. Schnabel ◽  
Joshua Pierce
Keyword(s):  
Staphylococcus Aureus ◽  
Human Health ◽  
Matrix Model ◽  
Bacterial Load ◽  
Collagen Matrix ◽  
Resistance Mechanisms ◽  
Novel Therapeutics ◽  
Innovative Treatment ◽  
Antibiotic Action ◽  
Biofilm Infection

<div>The failure of frontline antibiotics in the clinic is one of the most serious threats to human health and requires a multitude of novel therapeutics and innovative treatment approaches to curtail the growing crisis. In addition to traditional resistance mechanisms resulting in the lack of efficacy of many antibiotics, most chronic and recurring infections are further made tolerant to antibiotic action by the presence of biofilms. Herein, we report an expanded set of 5-benzylidene-4-oxazolidinones that are able to inhibit the formation of Staphylococcus aureus biofilms, disperse preformed biofilms and in combination with common antibiotics are able to significantly reduce the bacterial load in a robust collagen-matrix model of biofilm infection.</div>

scholarly journals Comment on “The phase diagram of the multi-matrix model with ABAB-interaction from functional renormalization”

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Carlos I. Perez-Sanchez
Keyword(s):  
Phase Diagram ◽  
Matrix Model ◽  
Loop Structure ◽  
The One

Abstract Recently, [JHEP12 131 (2020)] obtained (a similar, scaled version of) the (a, b)-phase diagram derived from the Kazakov-Zinn-Justin solution of the Hermitian two-matrix model with interactions$$ -\mathrm{Tr}\left\{\frac{a}{4}\left({A}^4+{B}^4\right)+\frac{b}{2} ABAB\right\}, $$ − Tr a 4 A 4 + B 4 + b 2 ABAB , starting from Functional Renormalization. We comment on something unexpected: the phase diagram of [JHEP12 131 (2020)] is based on a βb-function that does not have the one-loop structure of the Wetterich-Morris equation. This raises the question of how to reproduce the phase diagram from a set of β-functions that is, in its totality, consistent with Functional Renormalization. A non-minimalist, yet simple truncation that could lead to the phase diagram is provided. Additionally, we identify the ensemble for which the result of op. cit. would be entirely correct.

scholarly journals Genus expansion of matrix models and ћ expansion of KP hierarchy

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
A. Andreev ◽  
A. Popolitov ◽  
A. Sleptsov ◽  
A. Zhabin
Keyword(s):  
Matrix Models ◽  
Matrix Model ◽  
Special Interest ◽  
Hermitian Matrix ◽  
Geometric Meaning ◽  
Kp Hierarchy ◽  
Hurwitz Numbers ◽  
Kp Equations ◽  
Genus Expansion ◽  
Hermitian Matrix Model

Abstract We study ћ expansion of the KP hierarchy following Takasaki-Takebe [1] considering several examples of matrix model τ-functions with natural genus expansion. Among the examples there are solutions of KP equations of special interest, such as generating function for simple Hurwitz numbers, Hermitian matrix model, Kontsevich model and Brezin-Gross-Witten model. We show that all these models with parameter ћ are τ-functions of the ћ-KP hierarchy and the expansion in ћ for the ћ-KP coincides with the genus expansion for these models. Furthermore, we show a connection of recent papers considering the ћ-formulation of the KP hierarchy [2, 3] with original Takasaki-Takebe approach. We find that in this approach the recovery of enumerative geometric meaning of τ-functions is straightforward and algorithmic.

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