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Chris Berg

Publications and source records attributed to Chris Berg.

At least 19 recordsLinked to original sources
arXiv2023

Open Problems in DAOs

Decentralized autonomous organizations (DAOs) are a new, rapidly-growing class of organizations governed by smart contracts. Here we describe how researchers can contribute to the emerging science of DAOs and other digitally-constituted organizations. From granular privacy primitives to mechanism designs to model laws, we identify high-impact problems in the DAO ecosystem where existing gaps might be tackled through a new data set or by applying tools and ideas from existing research fields such as political science, computer science, economics, law, and organizational science. Our recommendations encompass exciting research questions as well as promising business opportunities. We call on the wider research community to join the global effort to invent the next generation of organizations.

cs.CY↗
arXiv2022

Reward Shaping for User Satisfaction in a REINFORCE Recommender

How might we design Reinforcement Learning (RL)-based recommenders that encourage aligning user trajectories with the underlying user satisfaction? Three research questions are key: (1) measuring user satisfaction, (2) combatting sparsity of satisfaction signals, and (3) adapting the training of the recommender agent to maximize satisfaction. For measurement, it has been found that surveys explicitly asking users to rate their experience with consumed items can provide valuable orthogonal information to the engagement/interaction data, acting as a proxy to the underlying user satisfaction. For sparsity, i.e, only being able to observe how satisfied users are with a tiny fraction of user-item interactions, imputation models can be useful in predicting satisfaction level for all items users have consumed. For learning satisfying recommender policies, we postulate that reward shaping in RL recommender agents is powerful for driving satisfying user experiences. Putting everything together, we propose to jointly learn a policy network and a satisfaction imputation network: The role of the imputation network is to learn which actions are satisfying to the user; while the policy network, built on top of REINFORCE, decides which items to recommend, with the reward utilizing the imputed satisfaction. We use both offline analysis and live experiments in an industrial large-scale recommendation platform to demonstrate the promise of our approach for satisfying user experiences.

cs.IR↗
arXiv2021

Quantum crypto-economics: Blockchain prediction markets for the evolution of quantum technology

Two of the most important technological advancements currently underway are the advent of quantum technologies, and the transitioning of global financial systems towards cryptographic assets, notably blockchain-based cryptocurrencies and smart contracts. There is, however, an important interplay between the two, given that, in due course, quantum technology will have the ability to directly compromise the cryptographic foundations of blockchain. We explore this complex interplay by building financial models for quantum failure in various scenarios, including pricing quantum risk premiums. We call this quantum crypto-economics.

q-fin.PR↗
arXiv2016

Multiplicative structures of the immaculate basis of non-commutative symmetric functions

We continue our development of a new basis for the algebra of non-commutative symmetric functions. This basis is analogous to the Schur basis for the algebra of symmetric functions, and it shares many of its wonderful properties. For instance, in this article we describe non-commutative versions of the Littlewood-Richardson rule and the Murnaghan-Nakayama rule. A surprising relation develops among non-commutative Littlewood-Richardson coefficients, which has implications to the commutative case. Finally, we interpret these new coefficients geometrically as the number of integer points inside a certain polytope.

math.CO↗
arXiv2014

Symmetries on the lattice of $k$-bounded partitions

In 2002 R. Suter identified a dihedral symmetry on certain order ideals in Young's lattice and gave a combinatorial action on the partitions in these order ideals. Viewing this result geometrically, the order ideals can be seen to be seen to be in bijection with the alcoves in a 2-fold dilation in the geometric realization of the affine symmetric group. By considering the m-fold dilation we observe a larger set of order ideals in the k-bounded partition lattice that was considered by L. Lapointe, A. Lascoux, and J. Morse in the study of k-Schur functions. We identify the order ideal and the cyclic action on it explicitly in a geometric and combinatorial form.

math.CO↗
arXiv2014

FindStat - the combinatorial statistics database

The FindStat project at www.FindStat.org provides an online platform for mathematicians, particularly for combinatorialists, to gather information about combinatorial statistics and their relations. This outline provides an overview over the project.

math.CO↗
arXiv2013

A lift of the Schur and Hall-Littlewood bases to non-commutative symmetric functions

We introduce a new basis of the non-commutative symmetric functions whose commutative images are Schur functions. Dually, we build a basis of the quasi-symmetric functions which expand positively in the fundamental quasi-symmetric functions and decompose Schur functions. We then use the basis to construct a non-commutative lift of the Hall-Littlewood symmetric functions with similar properties to their commutative counterparts.

math.CO↗
arXiv2013

The immaculate basis of the non-commutative symmetric functions

FPSAC 2013 Extended Abstract. We introduce a new basis of the non-commutative symmetric functions whose elements have Schur functions as their commutative images. Dually, we build a basis of the quasi-symmetric functions which expand positively in the fundamental quasi-symmetric functions and decompose Schur functions according to a signed combinatorial formula.

math.CO↗
arXiv2012

The down operator and expansions of near rectangular k-Schur functions

We prove that the Lam-Shimozono "down operator" on the affine Weyl group induces a derivation of the affine Fomin-Stanley subalgebra of the affine nilCoxeter algebra. We use this to verify a conjecture of Berg, Bergeron, Pon and Zabrocki describing the expansion of k-Schur functions of "near rectangles" in the affine nilCoxeter algebra. Consequently, we obtain a combinatorial interpretation of the corresponding k-Littlewood--Richardson coefficients.

math.CO↗
arXiv2011

Primitive orthogonal idempotents for R-trivial monoids

We construct a recursive formula for a complete system of primitive orthogonal idempotents for any $R$-trivial monoid. This uses the newly proved equivalence between the notions of $R$-trivial monoid and weakly ordered monoid.

math.RT↗
arXiv2011

($\ell,0)$-Carter partitions, a generating function, and their crystal theoretic interpretation

In this paper we give an alternate combinatorial description of the "$(\ell,0)$-JM partitions" (see \cite{F}) that are also $\ell$-regular. Our main theorem is the equivalence of our combinatoric and the one introduced by James and Mathas (\cite{JM}). The condition of being an $(\ell,0)$-JM partition is fundamentally related to the hook lengths of the partition. The representation-theoretic significance of their combinatoric on an $\ell$-regular partition is that it indicates the irreducibility of the corresponding specialized Specht module over the finite Hecke algebra (see \cite{JM}). We use our result to find a generating series which counts the number of such partitions, with respect to the statistic of a partition's first part. We then apply our description of these partitions to the crystal graph $B(Λ_0)$ of the basic representation of $\hat{\mathfrak{sl}_{\ell}}$, whose nodes are labeled by $\ell$-regular partitions. Here we give a fairly simple crystal-theoretic rule which generates all $\ell$-regular $(\ell,0)$-JM partitions in the graph $B(Λ_0)$. Finally, we mention how our construction can be generalized to recent results of M. Fayers (see \cite{F}) and S. Lyle (see \cite{L}) to count the total number of (not necessarily $\ell$-regular) Specht modules which stay irreducible at a primitive $\ell$th root of unity (for $\ell >2$).

math.CO↗
arXiv2011

The ladder crystal

n this paper I introduce a new description of the crystal $B(Λ_0)$ of $\hat{\mathfrak{sl}_\ell}$. As in the Misra-Miwa model of $B(Λ_0)$, the nodes of this crystal are indexed by partitions and the $i$-arrows correspond to adding a box of residue $i$. I then show that the two models are equivalent by interpreting the operation of regularization introduced by James as a crystal isomorphism.

math.CO↗