Piano Genie

We present Piano Genie, an intelligent controller which allows non-musicians to improvise on the piano. With Piano Genie, a user performs on a simple interface with eight buttons, and their performance is decoded into the space of plausible piano music in real time. To learn a suitable mapping procedure for this problem, we train recurrent neural network autoencoders with discrete bottlenecks: an encoder learns an appropriate sequence of buttons corresponding to a piano piece, and a decoder learns to map this sequence back to the original piece. During performance, we substitute a user's input for the encoder output, and play the decoder's prediction each time the user presses a button. To improve the intuitiveness of Piano Genie's performance behavior, we impose musically meaningful constraints over the encoder's outputs.Comment: Published as a conference paper at ACM IUI 201

The eleven antenna: a compact low-profile decade bandwidth dual polarized feed for reflector antennas

A novel dual polarized ultrawide-band (UWB) feed with a decade bandwidth is presented for use in both single and dual reflector antennas. The feed has nearly constant beam width and 11 dBi directivity over at least a decade bandwidth. The feed gives an aperture efficiency of the reflector of 66% or better over a decade bandwidth when the subtended angle toward the sub or main reflector is about 53°, and an overall efficiency better than 47% including mismatch. The return loss is better than 5 dB over a decade bandwidth. The calculated results have been verified with measurements on a linearly polarized lab model. The feed has no balun as it is intended to be integrated with an active 180° balun and receiver. The feed is referred to as the Eleven antenna because its basic configuration is two parallel dipoles 0.5 wavelengths apart and because it can be used over more than a decade bandwidth with 11 dBi directivity. We also believe that 11 dB return loss is achievable in the near future

Quantum speedups for linear programming via interior point methods

We describe a quantum algorithm based on an interior point method for solving a linear program with $n$ inequality constraints on $d$ variables. The algorithm explicitly returns a feasible solution that is $\varepsilon$-close to optimal, and runs in time $\sqrt{n} \cdot \mathrm{poly}(d,\log(n),\log(1/\varepsilon))$ which is sublinear for tall linear programs (i.e., $n \gg d$). Our algorithm speeds up the Newton step in the state-of-the-art interior point method of Lee and Sidford [FOCS~'14]. This requires us to efficiently approximate the Hessian and gradient of the barrier function, and these are our main contributions. To approximate the Hessian, we describe a quantum algorithm for the \emph{spectral approximation} of $A^T A$ for a tall matrix $A \in \mathbb R^{n \times d}$. The algorithm uses leverage score sampling in combination with Grover search, and returns a $\delta$-approximation by making $O(\sqrt{nd}/\delta)$ row queries to $A$. This generalizes an earlier quantum speedup for graph sparsification by Apers and de Wolf~[FOCS~'20]. To approximate the gradient, we use a recent quantum algorithm for multivariate mean estimation by Cornelissen, Hamoudi and Jerbi [STOC '22]. While a naive implementation introduces a dependence on the condition number of the Hessian, we avoid this by pre-conditioning our random variable using our quantum algorithm for spectral approximation

Winning by a Mile : A Mathematical Programming Approach to Reducing Distance and Ensuring Fairness in Travel in the FIFA World Cup

The FIFA World Cup presents a complex logistical challenge, featuring an intricate tournament schedule that requires teams to frequently move between their base camps and match venues. In this thesis, we explore the potential of mathematical programming as a tool to devise an optimal tournament schedule that reduces extensive travel and ensures fair travel distribution. We create a FIFA World Cup scheduling framework consisting of mixed integer linear programming models. The framework consists of a series of individual optimization models, crafted from the guidelines of the World Cup of 2014 and 2018. All models yield significantly improved objectives relative to the historical benchmarks of 2014 and 2018. For the models minimizing total distance traveled throughout the group stage, the results range from a decrease of 25% to 48% in distance covered compared to historical distances. For the models minimizing the distance between the least and most traveling teams among all teams, the results range from a decrease of 81% to 96% for this inner range compared to historical differences. For the models minimizing the distance between the least and most traveling teams within each group, the results range from a decrease of 83% to 98% for the sum of the groupwise inner ranges compared to the sum of the historical groupwise inner ranges. We further combine the individual objectives into a multi-objective model using the �- constraint method, thereby showcasing a Pareto front of candidate solutions that all yield results that surpass the historical benchmarks for both objectives simultaneously. Our findings strongly indicate that utilizing mathematical programming for the World Cup match scheduling process offers the potential to reduce the overall distances traveled while concurrently ensuring a more balanced distribution of travel burdens among the participants. We highlight the 2026 World Cup as an ideal prospect for implementing this approach.nhhma

Pseudospectral methods provide fast and accurate solutions for the horizontal infiltration equation

An extremely fast and accurate pseudospectral numerical method is presented, which can be used in inverse methods for estimating soil hydraulic parameters from horizontal infiltration or desorption experiments. Chebyshev polynomial dierentiation in conjunction with the flux concentration formulation of Philip (1973) results in a numerical solution of high order accuracy that is directly dependent on the number of Chebyshev nodes used. The level of accuracy (< 0:01% for 100 nodes) is confirmed through a comparison with two dierent, but numerically demanding, exact closed-form solutions where an infinite derivative occurs at either the wetting front or the soil surface. Application of our computationally ecient method to estimate soil hydraulic parameters is found to take less than one second using modest laptop computer resources. The pseudospectral method can also be applied to evaluate analytical approximations, and in particular, those of Parlange and Braddock (1980) and Parlange et al (1994) are chosen. It is shown that both these approximations produce excellent estimates of both the sorptivity and moisture profile across a wide range of initial and boundary conditions and numerous physically realistic diusivity functions

Ability Dispersion and Team Performance: a field experiment

This paper studies the impact of diversity in cognitive ability among members of a team on their performance. We conduct a large field experiment in which teams start up and manage real companies under identical circumstances. Exogenous variation in - otherwise random - team composition is imposed by assigning individuals to teams based on their measured cognitive abilities. The setting is one of business management practices in the longer run where tasks are diverse and involve complex decision-making. We propose a model in which greater ability dispersion generates greater knowledge for a team, but also increases the costs of monitoring necessitated by moral hazard. Consistent with the predictions of our model, we find that team performance as measured in terms of sales, profits and profits per share first increases, and then decreases, with ability dispersion. Teams with a moderate degree of ability dispersion also experience fewer dismissals due to fewer shirking members in those teams

A (simple) classical algorithm for estimating Betti numbers

We describe a simple algorithm for estimating the $k$-th normalized Betti number of a simplicial complex over $n$ elements using the path integral Monte Carlo method. For a general simplicial complex, the running time of our algorithm is $n^{O\left(\frac{1}{\sqrt{\gamma}}\log\frac{1}{\varepsilon}\right)}$ with $\gamma$ measuring the spectral gap of the combinatorial Laplacian and $\varepsilon \in (0,1)$ the additive precision. In the case of a clique complex, the running time of our algorithm improves to $\left(n/\lambda_{\max}\right)^{O\left(\frac{1}{\sqrt{\gamma}}\log\frac{1}{\varepsilon}\right)}$ with $\lambda_{\max} \geq k$, where $\lambda_{\max}$ is the maximum eigenvalue of the combinatorial Laplacian. Our algorithm provides a classical benchmark for a line of quantum algorithms for estimating Betti numbers. On clique complexes it matches their running time when, for example, $\gamma \in \Omega(1)$ and $k \in \Omega(n)$.Comment: v2: improved gap dependency by using Chebyshev polynomial