arXiv subjects

Sachio Ohkawa

Publications and source records attributed to Sachio Ohkawa.

4 recordsLinked to original sources

arXiv2026

Integrating Predictive Models into Two-Sided Recommendations: A Matching-Theoretic Approach

Two-sided platforms must recommend users to users, where matches (termed \emph{dates} in this paper) require mutual interest and activity on both sides. Naive ranking by predicted dating probabilities concentrates exposure on a small subset of highly responsive users, generating congestion and overstating efficiency. We model recommendation as a many-to-many matching problem and design integrators that map predicted login, like, and reciprocation probabilities into recommendations under attention constraints. We introduce \emph{effective dates}, a congestion-adjusted metric that discounts matches involving overloaded receivers. We then propose \emph{exposure-constrained deferred acceptance} (ECDA), which limits receiver exposure in terms of expected likes or dates rather than headcount. Using production-grade predictions from a large Japanese dating platform, we show in calibrated simulations that ECDA increases effective dates and receiver-side dating probability despite reducing total dates. A large-scale regional field experiment confirms these effects in practice, indicating that exposure control improves equity and early-stage matching efficiency without harming downstream engagement.

econ.GN↗

arXiv2017

Riemann-Hilbert correspondence for unit $F$-crystals on embeddable algebraic varieties

For a separated scheme $X$ of finite type over a perfect field $k$ of characteristic $p>0$ which admits an immersion into a proper smooth scheme over the truncated Witt ring $W_{n}$, we define the bounded derived category of locally finitely generated unit $F$-crystals with finite Tor-dimension on $X$ over $W_{n}$, independently of the choice of the immersion. Then we prove the anti-equivalence of this category with the bounded derived category of constructible étale sheaves of ${\mathbb Z}/{p^{n}{\mathbb Z}}$-modules with finite Tor dimension. We also discuss the relationship of $t$-structures on these derived categories when $n=1$. Our result is a generalization of the Riemann-Hilbert correspondence for unit $F$-crystals due to Emerton-Kisin to the case of (possibly singular) embeddable algebraic varieties in characteristic $p>0$.

math.AG↗

arXiv2015

On log local Cartier transform of higher level in characteristic $p$

In our previous paper, given an integral log smooth morphism $X\to S$ of fine log schemes of characteristic $p>0$, we studied the Azumaya nature of the sheaf of log differential operators of higher level and constructed a splitting module of it under an existence of a certain lifting modulo $p^{2}$. In this paper, under a certain liftability assumption which is stronger than our previous paper, we construct another splitting module of our Azumaya algebra over a scalar extension, which is smaller than our previous paper. As an application, we construct an equivalence, which we call the log local Cartier transform of higher level, between certain $\cal D$-modules and certain Higgs modules. We also discuss about the compatibility of the log Frobenius descent and the log local Cartier transform and the relation between the splitting module constructed in this paper and that constructed in the previous paper. Our result can be considered as a generalization of the result of Ogus-Vologodsky, Gros-Le Stum-Quirós to the case of log schemes and that of Schepler to the case of higher level.

math.AG↗

arXiv2014

On logarithmic nonabelian Hodge theory of higher level in characteristic p

Given a natural number $m$ and a log smooth integral morphism $X\to S$ of fine log schemes of characteristic $p>0$ with a lifting of its Frobenius pull-back $X'\to S$ modulo $p^{2}$, we use indexed algebras ${\cal A}_{X}^{gp}$, ${\cal B}_{X/S}^{(m+1)}$ of Lorenzon-Montagnon and the sheaf ${\cal D}_{X/S}^{(m)}$ of log differential operators of level $m$ of Berthelot-Montagnon to construct an equivalence between the category of certain indexed ${\cal A}_{X}^{gp}$-modules with ${\cal D}_{X/S}^{(m)}$-action and the category of certain indexed ${\cal B}_{X/S}^{(m+1)}$-modules with Higgs field. Our result is regarded as a level $m$ version of some results of Ogus-Vologodsky and Schepler.

math.NT↗