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We introduce JPC, a JAX library for training neural networks with Predictive Coding. JPC provides a simple, fast and flexible interface to train a variety of PC networks (PCNs) including discriminative, generative and hybrid models. Unlike existing libraries, JPC leverages ordinary differential equation solvers to integrate the gradient flow inference dynamics of PCNs. We find that a second-order solver achieves significantly faster runtimes compared to standard Euler integration, with comparable performance on a range of tasks and network depths. JPC also provides some theoretical tools that can be used to study PCNs. We hope that JPC will facilitate future research of PC. The code is available at https://github.com/thebuckleylab/jpc., Comment: 9 pages, 7 figures

We show that recent experiments in hybrid qubit-oscillator devices that measure the phase-space characteristic function of the oscillator via the qubit can be seen through the lens of functional calculus and path integrals, drawing a clear analogy with the generating functional of a quantum field theory. This connection suggests an expansion of the characteristic function in terms of Feynman diagrams, exposing the role of the real-time bosonic propagator, and identifying the external source functions with certain time-dependent couplings that can be controlled experimentally. By applying maximum-likelihood techniques, we show that the ``measurement'' of these Feynman diagrams can be reformulated as a problem of multi-parameter point estimation that takes as input a set of Ramsey-type measurements of the qubit. By numerical simulations that consider leading imperfections in trapped-ion devices, we identify the optimal regimes in which Feynman diagrams could be reconstructed from measured data with low systematic and stochastic errors. We discuss how these ideas can be generalized to finite temperatures via the Schwinger-Keldysh formalism, contributing to a bottom-up approach to probe quantum simulators of lattice field theories by systematically increasing the qubit-oscillator number.

Organisms have to keep track of the information in the environment that is relevant for adaptive behaviour. Transmitting information in an economical and efficient way becomes crucial for limited-resourced agents living in high-dimensional environments. The efficient coding hypothesis claims that organisms seek to maximize the information about the sensory input in an efficient manner. Under Bayesian inference, this means that the role of the brain is to efficiently allocate resources in order to make predictions about the hidden states that cause sensory data. However, neither of those frameworks accounts for how that information is exploited downstream, leaving aside the action-oriented role of the perceptual system. Rate-distortion theory, which defines optimal lossy compression under constraints, has gained attention as a formal framework to explore goal-oriented efficient coding. In this work, we explore action-centric representations in the context of rate-distortion theory. We also provide a mathematical definition of abstractions and we argue that, as a summary of the relevant details, they can be used to fix the content of action-centric representations. We model action-centric representations using VAEs and we find that such representations i) are efficient lossy compressions of the data; ii) capture the task-dependent invariances necessary to achieve successful behaviour; and iii) are not in service of reconstructing the data. Thus, we conclude that full reconstruction of the data is rarely needed to achieve optimal behaviour, consistent with a teleological approach to perception.

In construction projects, contingency reserves have traditionally been estimated based on a percentage of the total project cost, which is arbitrary and, thus, unreliable in practical cases. Monte Carlo simulation provides a more reliable estimation. However, works on this topic have focused exclusively on the effects of aleatoric uncertainty, but ignored the impacts of other uncertainty types. In this paper, we present a method to quantitatively determine project cost contingency reserves based on Monte Carlo Simulation that considers the impact of not only aleatoric uncertainty, but also of the effects of other uncertainty kinds (stochastic, epistemic) on the total project cost. The proposed method has been validated with a real-case construction project in Spain. The obtained results demonstrate that the approach will be helpful for construction Project Managers because the obtained cost contingency reserves are consistent with the actual uncertainty type that affects the risks identified in their projects., Comment: 15 pages

Project managers need to manage risks throughout the project lifecycle and, thus, need to know how changes in activity durations influence project duration and risk. We propose a new indicator (the Activity Risk Index, ARI) that measures the contribution of each activity to the total project risk while it is underway. In particular, the indicator informs us about what activities contribute the most to the project's uncertainty so that project managers can pay closer attention to the performance of these activities. The main difference between our indicator and other activity sensitivity metrics in the literature (e.g. cruciality, criticality, significance, or schedule sensitivity indices) is that our indicator is based on the Schedule Risk Baseline concept instead of on cost or schedule baselines. The new metric not only provides information at the beginning of the project, but also while it is underway. Furthermore, the ARI is the only one to offer a normalized result: if we add its value for each activity, the total sum is 100%., Comment: 22 pages

Obtaining a viable schedule baseline that meets all project constraints is one of the main issues for project managers. The literature on this topic focuses mainly on methods to obtain schedules that meet resource restrictions and, more recently, financial limitations. The methods provide different viable schedules for the same project, and the solutions with the shortest duration are considered the best-known schedule for that project. However, no tools currently select which schedule best performs in project risk terms. To bridge this gap, this paper aims to propose a method for selecting the project schedule with the highest probability of meeting the deadline of several alternative schedules with the same duration. To do so, we propose integrating aleatory uncertainty into project scheduling by quantifying the risk of several execution alternatives for the same project. The proposed method, tested with a well-known repository for schedule benchmarking, can be applied to any project type to help managers to select the project schedules from several alternatives with the same duration, but the lowest risk., Comment: 11 pages

In this paper, we apply a case study approach to advance current understanding of what effects public co-funding of R&D projects have on project team members' perceived complexity. We chose an R&D project carried out by an industrial SME in northern Spain. The chosen research strategy was a qualitative approach, and sixteen employees participated in the project. We held in-depth semi-structured interviews at the beginning and end of the co-funded part of the project. NVivo data analysis software was used for qualitative data analysis. Results showed a substantial increase in perceived complexity. We observed that this was due to unresolved tension between the requirements of the project's co-financing entity and normal SME working procedures. New working procedures needed to be developed in order to comply with the co-financing entity's requirements. However, overall perceived complexity significantly decreased once the co-financed part of the project was completed., Comment: 12 pages

Production planning in 3D printing factories brings new challenges among which the scheduling of parts to be produced stands out. A main issue is to increase the efficiency of the plant and 3D printers productivity. Planning, scheduling, and nesting in 3D printing are recurrent problems in the search for new techniques to promote the development of this technology. In this work, we address the problem for the suppliers that have to schedule their daily production. This problem is part of the LONJA3D model, a managed 3D printing market where the parts ordered by the customers are reorganized into new batches so that suppliers can optimize their production capacity. In this paper, we propose a method derived from the design of combinatorial auctions to solve the nesting problem in 3D printing. First, we propose the use of a heuristic to create potential manufacturing batches. Then, we compute the expected return for each batch. The selected batch should generate the highest income. Several experiments have been tested to validate the process. This method is a first approach to the planning problem in 3D printing and further research is proposed to improve the procedure, Comment: 12 pages

Large companies are fully engaged in their digital transformation, specifically in developing strategic Business Intelligence (BI) projects. They have a Digital Strategy and top-level executives managing the change. BI projects are also being carried out in SMEs. In this paper, we present the results of an interpretative study conducted on a sample of SMEs from different sectors carrying out BI projects. We study whether BI maturity models are valid for SMEs and their usefulness for analysing the projects and evaluating the results at the end of the project., Comment: 15 pages, in Spanish language

Purpose: The new competitive environment characterized by innovation and constant change is forcing a new organizational behavior. This requires a digital transformation of SMEs based on collective performance determinants. SMEs have particular characteristics that differentiate them from large companies and a model that allows them to identify, leverage and develop their digital capabilities can help them to advance in digital maturity. Design/methodology/approach: An in-depth review of the existing literature on digital transformation and organizational competence was carried out on Scopus and Web of Science to identify the digital challenges faced by SMEs, and what digital capabilities they have to develop to face these challenges. In order to obtain the necessary information for the refinement of organizational competence for digital transformation model, six experts were interviewed; three of them are academics and the other three are professionals with management responsibilities in SMEs. We used semi-structured interviews, to keep the interviews focused and facilitate cross-data analysis between experts. In addition, it allowed us the possibility of analyzing new relevant aspects that could arise during the interview. Findings: As a result of this study we have developed a refined model of organizational competence for digital transformation that allows SMEs to identify and develop the digital capabilities necessary to advance in the digital transformation, refined with the opinions of six experts consulted. We were able to observe the importance of organizational learning and organizational knowledge to advance the digital transformation of SMEs., Comment: 10 pages

Earned duration management (EDM) is a methodology for project schedule management (PSM) that can be considered an alternative to earned value management (EVM). EDM provides an estimation of deviations in schedule and a final project duration estimation. There is a key difference between EDM and EVM: In EDM, the value of activities is expressed as work periods; whereas in EVM, value is expressed in terms of cost. In this paper, we present how EDM can be applied to monitor and control stochastic projects. To explain the methodology, we use a real case study with a project that presents a high level of uncertainty and activities with random durations. We analyze the usability of this approach according to the activities network topology and compare the EVM and earned schedule methodology (ESM) for PSM., Comment: 14 pages

The project managers who deal with risk management are often faced with the difficult task of determining the relative importance of the various sources of risk that affect the project. This prioritisation is crucial to direct management efforts to ensure higher project profitability. Risk matrices are widely recognised tools by academics and practitioners in various sectors to assess and rank risks according to their likelihood of occurrence and impact on project objectives. However, the existing literature highlights several limitations to use the risk matrix. In response to the weaknesses of its use, this paper proposes a novel approach for prioritising project risks. Monte Carlo Simulation (MCS) is used to perform a quantitative prioritisation of risks with the simulation software MCSimulRisk. Together with the definition of project activities, the simulation includes the identified risks by modelling their probability and impact on cost and duration. With this novel methodology, a quantitative assessment of the impact of each risk is provided, as measured by the effect that it would have on project duration and its total cost. This allows the differentiation of critical risks according to their impact on project duration, which may differ if cost is taken as a priority objective. This proposal is interesting for project managers because they will, on the one hand, know the absolute impact of each risk on their project duration and cost objectives and, on the other hand, be able to discriminate the impacts of each risk independently on the duration objective and the cost objective., Comment: 13 pages

This paper presents a highly speculative model encompassing the cortex, thalamus, and hippocampus of the mammalian brain. While the majority of computational neuroscience models are founded upon empirical evidence, this model is predicated upon a hardware proposal for a machine learning accelerator. Such a device was designed to perform a specific task, such as speech recognition. The design process employed the principles and techniques typically used by computer architects in the design of devices such as processors. However, it also sought to maintain plausibility with biological systems in accordance with the current understanding of the mammalian brain. In the course of our research, we have identified a functional framework that may help to fill the gaps in current neuroscience, thereby facilitating the explanations for many elusive cognitive-level effects. This paper does not describe the device itself or the rationale behind the design decision, but instead, it presents a concise description of the derived model. In brief, the model provides a functional definition of the cortical column and its structural definition by the minicolumns. It also offers a descriptive model for the corticothalamic and corticostriatal loops, a functional proposal for the hippocampal complex, and a simplified view of the brainstem circuitry involved in auditory processing. The proposed model appears to provide an explanation for a number of cognitive phenomena, including some ERP effects, bottom-up and top-down attention, and the relationship between phenomena such as the cocktail party effect, anterograde and retrograde amnesia following hippocampal complex damage, and so forth.

This paper proposes a new approach to Machine Learning (ML) that focuses on unsupervised continuous context-dependent learning of complex patterns. Although the proposal is partly inspired by some of the current knowledge about the structural and functional properties of the mammalian brain, we do not claim that biological systems work in an analogous way (nor the opposite). Based on some properties of the cerebellar cortex and adjacent structures, a proposal suitable for practical problems is presented. A synthetic structure capable of identifying and predicting complex temporal series will be defined and experimentally tested. The system relies heavily on prediction to help identify and learn patterns based on previously acquired contextual knowledge. As a proof of concept, the proposed system is shown to be able to learn, identify and predict a remarkably complex temporal series such as human speech, with no prior knowledge. From raw data, without any adaptation in the core algorithm, the system is able to identify certain speech structures from a set of Spanish sentences. Unlike conventional ML, the proposal can learn with a reduced training set. Although the idea can be applied to a constrained problem, such as the detection of unknown vocabulary in a speech, it could be used in more applications, such as vision, or (by incorporating the missing biological periphery) fit into other ML techniques. Given the trivial computational primitives used, a potential hardware implementation will be remarkably frugal. Coincidentally, the proposed model not only conforms to a plausible functional framework for biological systems but may also explain many elusive cognitive phenomena.

We introduce Lindblad-like quantum tomography (L$\ell$QT) as a quantum characterization technique of time-correlated noise in quantum information processors. This approach enables the estimation of time-local master equations, including their possible negative decay rates, by maximizing a likelihood function subject to dynamical constraints. We discuss L$\ell$QT for the dephasing dynamics of single qubits in detail, which allows for a neat understanding of the importance of including multiple snapshots of the quantum evolution in the likelihood function, and how these need to be distributed in time depending on the noise characteristics. By a detailed comparative study employing both frequentist and Bayesian approaches, we assess the accuracy and precision of L$\ell$QT of a dephasing quantum dynamical map that goes beyond the Lindblad limit, focusing on two different microscopic noise models that can be realised in either trapped-ion or superconducting-circuit architectures. We explore the optimization of the distribution of measurement times to minimize the estimation errors, assessing the superiority of each learning scheme conditioned on the degree of non-Markovinity of the noise, and setting the stage for future experimental designs of non-Markovian quantum tomography.

Quantum sensors leverage matter's quantum properties to enable measurements with unprecedented spatial and spectral resolution. Among these sensors, those utilizing nitrogen-vacancy (NV) centers in diamond offer the distinct advantage of operating at room temperature. Nevertheless, signals received from NV centers are often complex, making interpretation challenging. This is especially relevant in low magnetic field scenarios, where standard approximations for modeling the system fail. Additionally, NV signals feature a prominent noise component. In this Letter, we present a signal-to-image deep learning model capable of automatically inferring the number of nuclear spins surrounding a NV sensor and the hyperfine couplings between the sensor and the nuclear spins. Our model is trained to operate effectively across various magnetic field scenarios, requires no prior knowledge of the involved nuclei, and is designed to handle noisy signals, leading to fast characterization of nuclear environments in real experimental conditions. With detailed numerical simulations, we test the performance of our model in scenarios involving varying numbers of nuclei, achieving an average error of less than $2\ \rm{kHz}$ in the estimated hyperfine constants., Comment: 4 pages, 3 figures + supplemental material

We present some simple proofs of the well-known expressions for \[ \zeta(2k) = \sum_{m=1}^\infty \frac{1}{m^{2k}}, \qquad \beta(2k+1) = \sum_{m=0}^\infty \frac{(-1)^m}{(2m+1)^{2k+1}}, \] where $k = 1,2,3,\dots$, in terms of the Bernoulli and Euler polynomials. The computation is done using only the defining properties of these polynomials and employing telescoping series. The same method also yields integral formulas for $\zeta(2k+1)$ and $\beta(2k)$. In addition, the method also applies to series of type \[ \sum_{m\in\mathbb{Z}} \frac{1}{(2m-\mu)^s}, \qquad \sum_{m\in\mathbb{Z}} \frac{(-1)^m}{(2m+1-\mu)^s}, \] in this case using Apostol-Bernoulli and Apostol-Euler polynomials., Comment: 24 pages, to appear in "Orthogonal Polynomials and Special Functions: In Memory of Jos\'e Carlos Petronilho''

We study three questions related to Machin's type formulas. The first one gives all two terms Machin formulas where both arctangent functions are evaluated $2$-integers, that is values of the form $b/2^a$ for some integers $a$ and~$b$. These formulas are computationally useful because multiplication or division by a power of two is a very fast operation for most computers. The second one presents a method for finding infinitely many formulas with $N$ terms. In the particular case $N=2$ the method is quite useful. It recovers most known formulas, gives some new ones, and allows to prove in an easy way that there are two terms Machin formulas with Lehmer measure as small as desired. Finally, we correct an oversight from previous result and give all Machin's type formulas with two terms involving arctangents of powers of the golden section., Comment: 22 pages, 3 figures