In this paper, we use a machine learning approach to predict the stationary distributions of the number of customers in a single-staiton multi server system. We consider two systems, the first is $c$ homogeneous servers, namely the $GI/GI/c$ queue. The second is a two-heterogeneous server system, namely the $GI/GI_i/2$ queue. We train a neural network for these queueing models, using the first four inter-arrival and service time moments. We demonstrate empirically that using the fifth moment and beyond does not increase accuracy. Compared to existing methods, we show that in terms of the stationary distribution and the mean value of the number of customers in a $GI/GI/c$ queue, we are state-of-the-art. Further, we are the only ones to predict the stationary distribution of the number of customers in the system in a $GI/GI_i/2$ queue. We conduct a thorough performance evaluation to assert that our model is accurate. In most cases, we demonstrate that our error is less than 5\%. Finally, we show that making inferences is very fast, where 5000 inferences can be made in parallel within a fraction of a second.

To democratize large language models (LLMs) to most natural languages, it is imperative to make these models capable of understanding and generating texts in many languages, in particular low-resource ones. While recent multilingual LLMs demonstrate remarkable performance in such capabilities, these LLMs still support a limited number of human languages due to the lack of training data for low-resource languages. Moreover, these LLMs are not yet aligned with human preference for downstream tasks, which is crucial for the success of LLMs in English. In this paper, we introduce xLLaMA-100 and xBLOOM-100 (collectively xLLMs-100), which scale the multilingual capabilities of LLaMA and BLOOM to 100 languages. To do so, we construct two datasets: a multilingual instruction dataset including 100 languages, which represents the largest language coverage to date, and a cross-lingual human feedback dataset encompassing 30 languages. We perform multilingual instruction tuning on the constructed instruction data and further align the LLMs with human feedback using the DPO algorithm on our cross-lingual human feedback dataset. We evaluate the multilingual understanding and generating capabilities of xLLMs-100 on five multilingual benchmarks. Experimental results show that xLLMs-100 consistently outperforms its peers across the benchmarks by considerable margins, defining a new state-of-the-art multilingual LLM that supports 100 languages.

The input/output properties of a 2 compartment model neuron are systematically explored. Taken from the work of MacGregor (MacGregor, 1987), the model neuron compartments contain several active conductances, including a potassium conductance in the dendritic compartment driven by the accumulation of intradendritic calcium. Dynamics of the conductances and potentials are governed by a set of coupled first order differential equations which are integrated numerically. There are a set of 17 internal parameters to this model, specificying conductance rate constants, time constants, thresholds, etc. To study parameter sensitivity, a set of trials were run in which the input driving the neuron is kept fixed while each internal parameter is varied with all others left fixed. To study the input/output relation, the input to the dendrite (a square wave) was varied (in frequency and magnitude) while all internal parameters of the system were left flXed, and the resulting output firing rate and bursting rate was counted. The input/output relation of the model neuron studied turns out to be much more sensitive to modulation of certain dendritic potassium current parameters than to plasticity of synapse efficacy per se (the amount of current influx due to synapse activation). This would in turn suggest, as has been recently observed experimentally, that the potassium current may be as or more important a focus of neural plasticity than synaptic efficacy.