Search Results (14)

As large language models process ever longer contexts, the positional encoding—most commonly rotary position embeddings (RoPEs)—must remain numerically trustworthy. We give an information-geometric analysis of why the attention matrix becomes ill-conditioned as the sequence length L grows. We first show that the tempting frequency-aliasing explanation fails, because RoPE’s multi-frequency code keeps positions well separated. The mechanism is statistical: at fixed softmax temperature the attention entropy grows like $logL$, and the rows spread their mass over a collision support (inverse participation ratio) that grows polynomially as $L^a$ ($a\approx 0.9$ measured), confining the matrix’s trailing singular values and producing a numerical-rank collapse. We prove, and confirm in 50-digit arithmetic, that the spectral condition number is intrinsically ill-posed here, so the numerical rank is the correct diagnostic. From the exact entropy–temperature identity $\mathrm{d}H/\mathrm{d}\beta =-\beta {\mathrm{Var}}_p\left(e\right)$ we derive the entropy-invariant schedule ${\beta }_{★}\left(L\right)={(L/L_{\mathrm{ref}})}^{c_0}$, Curvature-Corrected RoPE (CC-RoPE), and prove that in the diffuse near-circulant regime it eliminates the collapse at a characterised conditioning–mixing cost, whereas no relative-position-preserving warp can. The two signatures are further confirmed in a trained RoPE model (Pythia-160M); the downstream perplexity effect is framed as a falsifiable prediction. Full article

This study examines the Republic of Moldova’s macroeconomic vulnerability to external commodity price shocks (1992–2025) using the IMF’s Commodity Import Price Index (CIPI) combined with time series analysis and a mixed-frequency VAR model linking monthly price data to quarterly GDP. Four key findings emerge: First, vulnerability is event-driven rather than seasonal—irregular shocks dominate predictable patterns. Second, the CIPI exhibits highly persistent innovations and is non-stationary in levels, consistent with an I(1) process. This indicates that external import price shocks have long-lasting effects rather than dissipating quickly through mean reversion. Third, structural regimes have shifted, with the post-2020 period showing elevated volatility and higher baseline costs. Fourth, VAR impulse responses reveal a stop–go transmission: external price spikes initially raise nominal GDP through a valuation effect (higher lei value of unchanged import volumes), then feed into inflation, trigger policy tightening, and subsequently depress nominal activity while leaving persistent CPI level effects, which are the primary channel through which the shocks erode household welfare. Policy recommendations include: continuous CIPI monitoring for macro stress testing, buffer design accounting for persistent import-cost shifts, and structural measures such as energy diversification, domestic production capacity expansion, and commodity risk management tools to reduce exposure to global price volatility. Full article

This study examines the short- and medium-run linkages within Mexico’s energy–economy system under conditions of limited information. The analysis is motivated by the structural relevance of hydrocarbons for fiscal stability and by the growing need to understand how energy shocks propagate through economic and environmental subsystems. Using a vector autoregression (VAR) framework, nine interdependent macroeconomic and energy variables are jointly evaluated after harmonizing mixed-frequency data, standardizing series, and ensuring stationarity through ADF and KPSS tests. Dynamic responses are assessed through impulse response functions (IRFs), generalized IRFs (GIRFs), and forecast error variance decomposition (FEVD), complemented by Granger causality tests. Results show that oil rents exert a persistent and positive influence on GDP and public expenditure, while shocks to coal-fired generation and oil prices consistently reduce economic activity and increase emissions. Renewable capacity expands pro-cyclically but displays limited autonomous effects. Overall, the evidence reveals a fiscally and environmentally constrained system dominated by hydrocarbons, underscoring the importance of improving PEMEX’s operational efficiency, accelerating fiscal diversification, and strengthening institutional conditions for renewable investment. Full article

Against the accelerating of global climate change and carbon neutrality transitions, energy price volatility exerts complex effects on the employment dimension of economic sustainability through both industrial and agricultural channels as intermediaries. This study employed a mixed-frequency vector autoregression model to statistically analyze the weekly prices of four major industries and 24 sub-markets in China. The main outcome was the urban unemployment rate in China, and it was verified against the urban unemployment rates in 31 cities and the unemployment rates by age group (YUR/LUR). The study investigated the employment dimension of economic sustainability. Energy and energy metal prices represent the energy transition, while food and industrial goods prices characterize the intermediary linkages. Unemployment rates serve as the employment dimension of economic sustainability. The findings reveal bidirectional interactions and heterogeneous transmission mechanisms between prices and unemployment: energy prices exhibit weaker direct links to unemployment, partly influenced by demand inelasticity and policy adjustments; agricultural products face more persistent impacts, reflecting policy interventions and demand constraints; chemical products demonstrate the highest sensitivity and fastest response to unemployment shocks; metals show significant internal variations, with sub-market-level impacts being more pronounced yet shorter-lived. These insights advance climate and energy economics by guiding low-carbon transition policies, optimizing resource allocation, and managing energy market risks for resilient economic sustainability. Full article

Electricity price forecasting has been a topic of significant interest since the deregulation of electricity markets worldwide. The New Zealand electricity market is run primarily on renewable fuels, and so weather metrics have a significant impact on electricity price and volatility. In this paper, we employ a mixed-frequency vector autoregression (MF-VAR) framework where we propose a VAR specification to the reverse unrestricted mixed-data sampling (RU-MIDAS) model, called RU-MIDAS-VAR, to provide point forecasts of half-hourly electricity prices using several weather variables and electricity demand. A key focus of this study is the use of variational Bayes as an estimation technique and its comparison with other well-known Bayesian estimation methods. We separate forecasts for peak and off-peak periods in a day since we are primarily concerned with forecasts for peak periods. Our forecasts, which include peak and off-peak data, show that weather variables and demand as regressors can replicate some key characteristics of electricity prices. We also find the MF-VAR and RU-MIDAS-VAR models achieve similar forecast results. Using the LASSO, adaptive LASSO, and random subspace regression as dimension-reduction and variable selection methods helps to improve forecasts where random subspace methods perform well for large parameter sets while the LASSO significantly improves our forecasting results in all scenarios. Full article

This paper deals with the identifiability of VARMA models with VAR order greater than or equal to the MA order, in the context of mixed-frequency data (MFD) using extended Yule–Walker equations. The main contribution is that necessary and sufficient conditions for identifiability in the single-frequency data case are expressed in an original way and yield new results in the MFD case. We also provide two counterexamples that answer an open question in this topic about whether certain sufficient conditions are necessary for identifiability. Therefore, this paper expands the set of models that can be identified with MFD using extended Yule–Walker equations. The main idea is that with MFD, some autocovariance blocks are not available from observed variables and, in some cases, the new conditions in this paper can be used to reconstruct all the non-available covariance blocks from available covariance blocks. Full article

Investigating the essential impact of the cryptocurrency market on carbon emissions is significant for the U.S. to realize carbon neutrality. This exploration employs low-frequency vector auto-regression (LF-VAR) and mixed-frequency VAR (MF-VAR) models to capture the complicated interrelationship between cryptocurrency policy uncertainty (CPU) and carbon emission (CE) and to answer the question of whether cryptocurrency policy uncertainty could facilitate U.S. carbon neutrality. By comparison, the MF-VAR model possesses a higher explanatory power than the LF-VAR model; the former’s impulse response indicates a negative CPU effect on CE, suggesting that cryptocurrency policy uncertainty is a promoter for the U.S. to realize the goal of carbon neutrality. In turn, CE positively impacts CPU, revealing that mass carbon emissions would raise public and national concerns about the environmental damages caused by cryptocurrency transactions and mining. Furthermore, CPU also has a mediation effect on CE; that is, CPU could affect CE through the oil price (OP). In the context of a more uncertain cryptocurrency market, valuable insights for the U.S. could be offered to realize carbon neutrality by reducing the traditional energy consumption and carbon emissions of cryptocurrency trading and mining. Full article

As the basic raw materials of economic activities, major commodities prices have a significant impact on the real economy. Due to the impact of the COVID-19 pandemic, major commodities prices have been fluctuating sharply in a “deep V” pattern since 2020. Therefore, accurately grasping the risk linkage between commodity markets and the macroeconomy is the key to preventing systemic risk and maintaining the smooth operation of the economy. Based on the MF-VAR model, this paper analyzed the risk contagion between China’s commodity markets and macroeconomic sectors from the perspective of volatility spillover, focusing on risk spillover and its dynamic evolution during the COVID-19 pandemic, and deeply analyzed the transmission mechanism of risk spillover based on the mixed-frequency causality test method. Our findings show that China’s commodity markets are the net exporter of risk contagion and that all macroeconomic sectors are the net recipient of risk contagion. During the period of COVID-19, the risk contagion effect was significantly intensified. The fluctuation of the commodity markets has a long-lasting negative impact on the investment sector and has caused changes in macroeconomic sectors, such as the reduction of medium- and long-term loans, the reduction of money circulation speed, and the weakening of micro-individual consumption willingness. The results of causality analysis show that wealth, interest rate, and expectation effects are present in the risk contagion between the commodity markets and macroeconomic sectors. While being directly or indirectly impacted by the commodity markets, each macroeconomic sector also generates adverse feedback to the commodity markets. The complete description of the risk contagion between the commodity markets and the macro economy has guiding significance for regulatory authorities to improve risk control policies and reinforce the macro regulatory system. Full article

Improving air quality, reducing greenhouse gas emissions, and achieving independence from fossil fuels have led most countries towards deploying solar photovoltaics (PV) in the power distribution grid and electrifying the transportation fleet. Internal combustion engine (ICE) vehicles are, in particular, one of the main culprits of injecting greenhouse gas emissions into the atmosphere, making electric vehicles (EVs) an important tool in combating climate change. Despite their considerable environmental and economic benefits, the integration of PVs and EVs can introduce unique operational challenges for the power distribution grid. If not coordinated, high penetration of PVs and EVs can result in variety of power quality issues, such as instances of overvoltage and undervoltage, frequency fluctuations, and/or increased losses. This paper proposes a mixed-integer multi-objective nonlinear optimization model for optimal energy dispatch in a power distribution grid with high penetration of PV and EV resources. The model proposed here is an extension of the traditional voltage and var optimization (VVO) into a comprehensive and coordinated control of voltage, active power, and reactive power. A modified version of the IEEE 123-bus test distribution system is used to demonstrate the effectiveness of the proposed solution. Full article

Background: Time series analyses on the relationship between nurse staffing and inpatient care quality are rare due to inconsistent frequencies of data between common observations of nurse-staffing (e.g., monthly) and inpatient care quality indicators (e.g., quarterly). Methods: In order to deal with the issue of mixed frequency data, this research adopted the MF-VAR model to explore causal relationships among nurse staffing, inpatient care quality, and hospital competition under the global budget payment scheme of Taiwan’s healthcare system. Results: Our results identified bi-directional causation between nurse staffing and patient outcomes and one-way Granger causality running between nurse staffing and reimbursement payments for inpatient care services. Impulse-response analyses found positive (negative) effects of the patient-to-nurse ratio on adverse patient outcomes (reimbursement payments) in all types of hospitals and detrimental effects of adverse patient outcomes on the patient-to-nurse ratio in medical centers and regional hospitals across a 12-month period. Conclusions: These findings suggest that nurse staffing is an essential determinant of both patient outcomes and reimbursement payments. Strategic policies such as direct subsidy and hospital accreditation for appropriate nurse staffing levels should be implemented for medical centers and regional hospitals to mitigate the harmful effects of adverse patient outcomes on nurse staffing. Full article

The most recent climate change scenarios show that Southern and Eastern Europe will be affected by a significant increase in temperature and drought frequency by the end of the 21st century. Romania has already recorded very high temperatures and long periods of drought over recent decades, the most affected regions being the south, west and east of the country. Considering that successful forest management requires suitable species and high-quality reproductive material for reforestation, the aim of this study was to evaluate and compare the growth and drought response of Douglas fir (Pseudotsuga menziessi var. menziesii) and Norway spruce (Picea abies) in two stands installed at the end of the 19th century in western Romania. The growth traits, wood characteristics and drought parameters (resistance, recovery, resilience and relative resilience) of Douglas fir and Norway spruce trees have been analyzed and compared. The climate–growth relationship was determined using growth response functions over the period 1938–2017. Additionally, to simulate the potential impact of climate change on Douglas fir in this region, the RCP4.5 scenario was used over two periods: 2041–2070 and 2071–2100. The results reveal that Douglas fir has an exceptional growth capacity, overcoming the Norway spruce since the early ages in both site conditions. The highest growth performances were seen in the low-productivity site. From analyzing the responses to drought events, considerable differences were found between species. The results highlight the high resistance and relative resilience to extreme droughts of Douglas fir compared to Norway spruce. However, autumn–winter temperatures play an important role in the adaptation of Douglas fir to site conditions in Romania. The use of appropriate provenances of Douglas fir in mixed stands with native broadleaved species may be an option for climatically exposed sites, thus increasing the value of these stands. Full article

Wild bitter gourd (Momordica charantia L. var. abbreviata S.) is a kind of Chinese herbal medicine and is also a vegetable and fruit that people eat daily. Wild bitter gourd has many bioactive components, such as saponin, polysaccharide, and protein, and the extract is used to adjust blood sugar in patients with diabetes. The objective of this study was to investigate simultaneous hot air-assisted radio frequency (HARF) drying and pasteurization for bitter gourd extract, and then to evaluate its effects on blood sugar of type II diabetic mice. The results showed that the solid–liquid ratio of the wild bitter gourd powder to water was 1:10 and it was extracted using focused ultrasonic extraction (FUE) for only 10 min with 70 °C water. Then, 1 kg of concentrated bitter gourd extract was mixed with soybean fiber powder at a ratio of 2:1.1. It was dried by HARF, and the temperature of the sample could reach above 80 °C in only 12 min to simultaneously reduce moisture content (wet basis) from 58% to 15% and achieve a pasteurization effect to significantly reduce the total bacterial and mold counts. Type II diabetic mice induced by nicotinamide and streptozocin (STZ) for two weeks and then were fed four-week feeds containing 5% RF-dried wild gourd extract did not raise fasting blood glucose. Therefore, the dried powder of wild bitter gourd extracts by HARF drying had a hypoglycemic effect. Full article

Nitrous oxide (N₂O) is one of the main greenhouse gases and its emissions from vegetable production systems have brought a sustainability challenge. The objective of this study was to evaluate the potential of reducing N₂O emissions from silt loam soil by mixing nitrogen (N)-rich broccoli (Brassica oleracea var. italica) residue with wheat straw or water-washed wheat straw. An experiment was conducted in randomized complete block design with five treatments; unamended or control (BS), wheat straw (+S), broccoli residue (+CR), broccoli residue and wheat straw (+CR+S) and broccoli residue and washed wheat straw (+CR+Sw) and was replicated four times. The +CR and +S were added at the rate of 3.5 kg and 2.0 kg fresh matter m⁻² and their mixtures, +CR+S and +CR+Sw, were incorporated in 3.5 kg of silt loam soil at 60% water-filled pore space (WFPS) and packed in soil microcosms. Nitrous oxide emissions were measured once a day during the 14-day of study period. Daily fluxes of N₂O were found to be reduced on +CR+W and +CR+Sw when compared to single-amended +CR treatment. Similarly, N₂O fluxes on +CR+Sw (2772 µg N m⁻² h⁻¹) were significantly lower than +CR+S (3606 µg N m⁻² h⁻¹) soon after the amendment but did not vary significantly thereafter. Moreover, the amendment mixture, +CR+S and +Cr+Sw, resulted in lower net N₂O emissions by 73.3% and 74.2%, respectively, relative to +CR treatment. While the results clearly suggest that the +CR+S or +CR+Sw reduced N₂O emissions, it necessitated further studies, possibly by increasing the frequency of sampling to clarify if washed wheat straw would further mitigate N₂O emissions from the vegetable production system. Full article

Management practices that promote dual-purpose use of cover crops as forage and soil cover can encourage adoption in mixed smallholder (SH) farming systems. This study investigated the feasibility of dual-purpose use of forage sorghum (Sorghum bicolor x Sorghum bicolor var. sudanense) by testing the effects of clipping frequency and nitrogen (N) topdressing on the root biomass, crude protein (CP), acid detergent (ADF), and neutral detergent fiber (NDF) in the greenhouse and vegetative biomass on the experimental farm station. Four levels of clipping were tested: not clipped (C1), clipped once (C2), twice (C3), and thrice (C4). Nitrogen topdressing had two levels: with (N1) and without (N0) recommended supplementary N. Results show that absence of N topdressing significantly (p < 0.05) increased root biomass in C2, while increasing clipping frequency significantly (p < 0.001) decreased root biomass. During the growing period, N topdressing significantly (p < 0.001) increased CP content in C3 and C4 and NDF (p < 0.01) content in C4. At the termination stage, there was a significant interaction between clipping frequency and N topdressing on the biomass yield obtained in both 2016–2017 (p < 0.05) and 2017–2018 (p < 0.001), respectively. Clipping twice and N topdressing emerged as the best management practice for the dual-purpose of soil cover and livestock feed. Full article