Estimation Of Products Research Articles

Sampling Methods for Inner Product Sketching

Recently, Bessa et al. (PODS 2023) showed that sketches based on coordinated weighted sampling theoretically and empirically outperform popular linear sketching methods like Johnson-Lindentrauss projection and CountSketch for the ubiquitous problem of inner product estimation. We further develop this finding by introducing and analyzing two alternative sampling-based methods. In contrast to the computationally expensive algorithm in Bessa et al., our methods run in linear time (to compute the sketch) and perform better in practice, significantly beating linear sketching on a variety of tasks. For example, they provide state-of-the-art results for estimating the correlation between columns in unjoined tables, a problem that we show how to reduce to inner product estimation in a black-box way. While based on known sampling techniques (threshold and priority sampling) we introduce significant new theoretical analysis to prove approximation guarantees for our methods.

Determinants of Labor Productivity of Turkish Manufacturing Sectors: The Role of Global Value Chain Participation

Purpose: This paper investigates the determinants of labor productivity of Turkish manufacturing sectors by taking into account both the global value chain (GVC) participation and the research and development (R&D) expenditure for the period of 1995-2018. Methodology: To analyze the determinants of labor productivity in Turkish manufacturing sectors, we specify the labor productivity model and estimate this empirical model by the Ordinary Least Squares (OLS) and Two-Stage Least Squares (2SLS) methods. Findings: Our estimation results indicate that while simple forward GVC participation enhances the labor productivity of Turkish high-tech manufacturing sectors if they trade with developing countries, complex forward GVC participation increases productivity regardless of trading partners. For low-tech sectors, there is no significant impact of GVCs or R&D on productivity. There is no significant impact of backward GVC participation and sectoral R&D intensity on labor productivity. These significant results provide strong evidence for the importance of deeper involvement of high-tech sectors in GVCs for higher sectoral productivity. Given the strong heterogeneity in terms of sectors and trading partners, specific policies should be targeted to benefit from the productivity gains of the global value chains. Originality: This study contributes to the current studies by focusing on disaggregated measures of GVC participation indices and enlarges the empirical analysis by considering the heterogeneity in trading partners (developed and developing trading partners).

On the dynamic asymptotic dimension of étale groupoids

We investigate the dynamic asymptotic dimension for étale groupoids introduced by Guentner, Willett and Yu. In particular, we establish several permanence properties, including estimates for products and unions of groupoids. We also establish invariance of the dynamic asymptotic dimension under Morita equivalence. In the second part of the article, we consider a canonical coarse structure on an étale groupoid, and compare the asymptotic dimension of the resulting coarse space with the dynamic asymptotic dimension of the underlying groupoid.

Simultaneous Determination of Fipronil, Permethrin, and Their Key Related Substances in a Topical Drug Product by a Single Stability-Indicating High-Performance Liquid Chromatography Method.

The topical veterinary drug product containing fipronil and permethrin provides an effective repellent protection and high insecticidal efficacy for dogs. The objective of this study was to develop a stability-indicating high-performance liquid chromatography (HPLC) method for simultaneous detection and quantification of fipronil, permethrin, their key degradation products, and butylated hydroxytoluene (BHT) in a topical drug product. The two active ingredients, their degradation products, and the antioxidant (BHT) were separated by a gradient elution on a Phenomenex Kinetex C18 column (150 × 3 mm, 2.6 µm particle size) maintained at 37°C with H2O acetonitrile isopropyl alcohol 85% H3PO4 (65.5 + 32.5 + 4/0.0053, v/v/v/v) as mobile phase A and acetonitrile (100%) as mobile phase B. The flow rate was 0.9 mL/min, and analytes were detected and quantified at 235 nm. The specificity of the method was demonstrated by adequate separation of fipronil, permethrin, their degradation products, and BHT in the forced degraded finished product. The linearity of the method was demonstrated in the range of 0.2% to 150% of target analytical concentration of both active ingredients and 50% to 150% for BHT. Excellent recoveries of fipronil, permethrin, and BHT in placebo spiked active ingredient solutions in the linearity range showed sufficient accuracy of the method. The LOQ and LOD of the method were determined to be 0.2% and 0.07% of the analytical concentration. A robustness study did not identify any critical parameter that adversely affected the separation and quantification. Here, we report the development and validation of a robust, stability-indicating HPLC method for identification and assay of fipronil, permethrin, and BHT, including estimation of fipronil's and permethrin's degradation products in a topical drug product for dogs. The new HPLC method permits the acquisition of data for all analytes of interest for a topical finished drug product containing fipronil, permethrin, and BHT.

Estimation of Advanced Glycation End Products in Selected Foods and Beverages by Spectrofluorimetry and ELISA.

Advanced glycation end products (AGEs) are formed within the body as a part of normal metabolism and are also the by-products of cooking food. The elevated levels of AGEs in the body are considered pathogenic. The modern diets contain high levels of AGEs which are getting incorporated into the body AGEs pool and contribute to post-diabetic and age-related complications. The objective of the present study is to estimate the cross-linked AGEs (AGE-fluorescence) and the more stable carboxymethyl-lysine (CML) by spectrofluorimetry and ELISA in 58 kinds of foods in India. It was evident from the results that the foods cooked at higher temperatures showed high levels of AGEs. Among the studied foods, the highest fluorescence was observed in Biscuits 2 (362 AU), and the highest level of carboxymethyl lysine (CML) was found in Soya milk (659.3 ng/g). However, there was less correlation between the AGE-fluorescence and the CML content of the food samples. Processed food such as tomato sauce, chilli sauce, and cheese, along with western foods like chicken nuggets, pizza, and biscuits like Biscuits 2, are known to contain high levels of AGEs. In the present study a preliminary database of AGE-fluorescence and CML content of 58 foods was developed, which is the first attempt among Indian foods. Furthermore, elaborated database can be developed including maximum consumed foods in India which will help in suggesting a better diet for the diabetic population.

Significant dark inorganic carbon fixation in the euphotic zone of an oligotrophic sea

AbstractEstimates of primary productivity have traditionally disregarded dark inorganic carbon fixation by marine microorganisms. Currently, only limited data are available from different systems on this potentially ecologically important process. We present monthly dark inorganic carbon fixation and photosynthetic rates from the euphotic layer of the northern Gulf of Aqaba collected over a decade between 2010 and 2020. Averaged dark inorganic carbon fixation rates from surface to 100 m depth, ranged from 99 to 173 mg C m−2 d−1, which corresponds to ~ 43% of the annual primary productivity at this location. The lowest dark inorganic carbon fixation rates were found during winter, contributing ~ 7.5% of the integrated primary productivity. During the oligotrophic summer, dark inorganic carbon fixation comprised a larger fraction of the integrated primary productivity estimated as ~ 12%. In accordance, dark inorganic carbon fixation contributed ~ 6% to the particulate organic carbon flux during the winter and ~ 30% during summertime. Complimentary nutrient‐enrichment bioassays of seawater from 5 m show that dissolved organic nutrient enrichment (P and C based) significantly elevates dark inorganic carbon fixation, whereas addition of dissolved inorganic nutrients (, , or both) significantly increased photosynthesis but to a lesser extent dark inorganic carbon fixation. These results suggest that dark inorganic carbon fixation may be an important biochemical process throughout the euphotic zone of oligotrophic seas, and thus should be incorporated into oceanic carbon production estimates.

Blind deconvolution decreases requirements on temporal resolution of DCE-MRI: Application to 2nd generation pharmacokinetic modeling

PurposeDynamic Contrast-Enhanced (DCE) MRI with 2nd generation pharmacokinetic models provides estimates of plasma flow and permeability surface-area product in contrast to the broadly used 1st generation models (e.g. the Tofts models). However, the use of 2nd generation models requires higher frequency with which the dynamic images are acquired (around 1.5 s per image). Blind deconvolution can decrease the demands on temporal resolution as shown previously for one of the 1st generation models. Here, the temporal-resolution requirements achievable for blind deconvolution with a 2nd generation model are studied. MethodsThe 2nd generation model is formulated as the distributed-capillary adiabatic-tissue-homogeneity (DCATH) model. Blind deconvolution is based on Parker's model of the arterial input function. The accuracy and precision of the estimated arterial input functions and the perfusion parameters is evaluated on synthetic and real clinical datasets with different levels of the temporal resolution. ResultsThe estimated arterial input functions remained unchanged from their reference high-temporal-resolution estimates (obtained with the sampling interval around 1 s) when increasing the sampling interval up to about 5 s for synthetic data and up to 3.6–4.8 s for real data. Further increasing of the sampling intervals led to systematic distortions, such as lowering and broadening of the 1st pass peak. The resulting perfusion-parameter estimation error was below 10% for the sampling intervals up to 3 s (synthetic data), in line with the real data perfusion-parameter boxplots which remained unchanged up to the sampling interval 3.6 s. ConclusionWe show that use of blind deconvolution decreases the demands on temporal resolution in DCE-MRI from about 1.5 s (in case of measured arterial input functions) to 3–4 s. This can be exploited in increased spatial resolution or larger organ coverage.

Irrigation water economic value and productivity: An econometric estimation for maize grain production in Italy

Climate change, characterized by rising temperatures and limited precipitation, has intensified the demand for irrigation water while simultaneously restricting its availability. This challenge poses significant risks to agricultural and food production, particularly in the Mediterranean regions where, recently, water deficits have led to substantial production losses and quality issues. Water is a critical determinant of crops' economic viability, especially for water-intensive crops, making it essential to estimate its economic relevance, especially in the absence of reliable water market prices. This study has two primary objectives: first, to evaluate the shadow price of irrigation water for maize grain at the farm level, which is defined as the value generated by the marginal unit of water consumed; and second, to analyse its heterogeneity. Leveraging a Farm Accountancy Data Network (FADN) panel of 1625 Italian farms over a decade (2010–2020), an econometric production function approach is employed. Moreover, quantile regressions reveal variations in the shadow price linked to geographical, managerial, and structural farm characteristics. Our findings underscore water’s key role in economically viable maize grain production, significantly enhancing the productivity of other inputs like fertilizers and pesticides. The average shadow price is 0.29 €/m³, with a median of 0.20 €/m³ and water total productivity accounts for one-third of maize’s average gross output. Quantile regressions uncover how factors like geographic location, altitude, farm management, irrigation water source, and farm size influence the distribution of water productivity, reflecting either efficient use or scarcity of this resource. Our estimation provides valuable insights for policymakers by offering accurate shadow price estimates for irrigation water in Italian maize grain production. Furthermore, it enhances our understanding of irrigation water’s role in the economic viability of this crop, while contributing to support evidence-based water management strategies, identifying vulnerable areas and farms and allowing for future methodological developments.

Redefining Radiation Metrics: Evaluating Actual Doses in Computed Tomography Scans.

Computed tomography (CT) contributes significantly to the collective dose from medical sources, raising concerns about potential health risks. However, existing radiation dose estimation tools, such as volume computed tomography dose index (CTDIvol), dose-length product (DLP), effective dose (ED), and size-specific dose estimate (SSDE), have limitations in accurately reflecting patient exposure. This study introduces a new parameter, size-specific dose-length product (DLPss), aiming to enhance the precision of radiation dose estimation in real-life scenarios. A retrospective analysis of 134 chest CT studies was conducted. Relationships between CTDIvol and anthropometric parameters were examined, and SSDE was calculated based on effective diameter. Additionally, the novel parameter, DLPss, was introduced, considering scan length and cross-sectional dimensions. Analysis reveals variations in scan length, effective diameter, and CTDIvol between genders. Strong correlations were observed between CTDIvol and effective diameter, particularly in men. The average CTDIvol for the entire group was 7.83 ± 2.92 mGy, with statistically significant differences between women (7.38 ± 3.23 mGy) and men (8.30 ± 2.49 mGy). SSDE values showed significant gender differences, with men exhibiting higher values. The average SSDE values for women and men were 9.15 ± 2.5 mGy and 9.6 ± 2.09 mGy, respectively, with a statistically significant difference (p = 0.03). The newly introduced DLPss values ranged around 343.90 ± 81.66 mGy·cm for the entire group, with statistically significant differences between women (323.53 ± 78.69 mGy·cm) and men (364.89 ± 79.87 mGy·cm) (p < 0.05), providing a comprehensive assessment of total radiation dose. The study highlights the need for accurate radiation dose estimation, emphasizing the impact of CT examination parameters on dose variability. The proposed DLPss parameter offers a promising approach to enhancing precision in assessing radiation risk during CT scans. Further research is warranted to explore additional parameters for a comprehensive understanding of radiation exposure and to optimize imaging protocols for patient safety.

Estimation of heterogeneous population variance using memory-type estimators based on EWMA statistic in the presence of measurement error for time-scaled surveys

In this present article, we have suggested memory-type ratio, exponential ratio, product and exponential product estimators based on exponentially weighted moving average statistic for the estimation of heterogeneous population variance using stratified sampling design in presence of measurement error for time-scaled surveys. Mathematical expressions of approximate mean square error are derived using Taylor and exponential expansions for the proposed memory-type estimators. We have also discussed the situations in which the memory-type estimators would perform efficiently than the conventional estimators. The results of extensive simulation study revealed that the proposed memory-type estimators based exponentially weighted moving average statistic would perform better than the conventional estimators in the presence measurement error for time-scaled surveys under certain condition.

On the Value of a Premium College Football Player: Evaluating the Literature

Over the past decade, the issue of player compensation in college sports has been the subject of several successful legal challenges. Athletes contend that the compensation they receive falls significantly short of the value they generate, attributing this gap to unlawful National Collegiate Athletic Association restrictions. Numerous tools exist in the sports economic literature that estimate the value of college athletes, with an emphasized focus toward premium college football players. In addition to providing updated estimate of player marginal revenue product (MRP), we review past and contemporary methodologies for estimating college player MRPs. We contend that, while presenting some evidence that restrictions on player compensation resulted in the extraction of the majority of the value generated by top college athletes, existing methods leave considerable uncertainty over the magnitude of exploitation.

АНАЛІЗ ТА ОЦІНКА ПІДПРИЄМНИЦЬКОГО ПОТЕНЦІАЛУ РЕГІОНУ

The article analyzes and evaluates the entrepreneurial potential of the region. Structural components of the entrepreneurial potential of the region were analyzed: financial potential, production potential, innovation potential, infrastructure potential, labor potential. The integral index of the entrepreneurial potential of the region was calculated. Regions were grouped according to the level of entrepreneurial potential in the pre-war period. Two groups of regions are distinguished by the level of entrepreneurial potential: regions with a low level of entrepreneurial potential and regions with a high level of entrepreneurial potential. An estimate of the gross regional product per person in the pre-war period was made. A comparison of the levels of entrepreneurial potential of the regions and the level of GRP in the pre-war period was carried out. The results of the grouping showed that the values of high levels of entrepreneurial potential and gross regional product are correlated only in the city of Kyiv. The rest of the results of the analysis show the ineffectiveness of using the entrepreneurial potential of the regions of the state. The reasons for ineffective use of the entrepreneurial potential of the regions of the state are outlined, including: low level of attracting funds for innovative activities; lack of incentives to increase the innovative activity of business entities; low level of production of innovative products; lack of incentives to create new jobs; low level of remuneration of enterprise personnel; migration outflow of qualified labor force abroad; insufficient level of utilization of regional production capacities; a drop in production volumes of industrial, construction and agricultural products; low level of development of infrastructural support for the development of entrepreneurial potential; low level of efficiency of using the infrastructure potential of the region; low amount of investment income; low level of investment attractiveness of the territories of the state as a result of military operations

Addressing endogeneity in marginal revenue product estimates of shirking in Major League Baseball

PurposeWhile much of the literature testing for shirking by professional athletes have used performance metrics, some works have quantified shirking in dollar terms by comparing salary to estimated marginal revenue product (MRP). However, Ordinary Least Squares (OLS) approaches to measuring shirking by comparing salary to MRP have an endogeneity problem, as salary and contract length are determined simultaneously. We test for shirking in Major League Baseball (MLB) using an MRP approach, addressing this potential endogeneity.Design/methodology/approachThis paper uses instrumental variables regression to address potential endogeneity using MLB season-level player and team data from 2010 to 2017.FindingsUsing OLS regression, the impact of an additional year of guaranteed contract on shirking is estimated at approximately $1m in 2010 US dollars, and the impact of having a long-term contract is estimated at $5m, estimates comparable to those in the literature. Using instrumental variables regression, these impacts increase to $1.6m and over $9m in 2010 dollars.Practical implicationsGiven large, causal shirking estimates, profit maximizing sports organizations should take caution when negotiating long-term contracts. These findings also have important implications for other labor market settings where workers feel job security.Originality/valueTo our knowledge, this is the first work testing for shirking in sports using an MRP approach which uses instrumental variables regression to address potential endogeneity.

Experience in Measuring Estimates of Russian GDP Dynamics Using Double Deflation Approach

When constructing estimates of gross domestic product (GDP) and gross value added (GVA) at constant prices, three approaches or a combination of them are used: extrapolation, simple deflation and double deflation. The latter approach is considered preferable, but is not yet used in Russian statistics. The article is devoted to the issues of constructing estimates of GDP and GVA dynamics for the Russian Federation using double deflation. The interest in constructing such estimates is due to the possibility of taking into account the dependence of production on domestic and import supplies, which the other two approaches lack. Received for the period from 2011 to 2016 estimates were compared with official indicators for the overall economy, the service sector, and for mining and manufacturing.From 2011 to 2016 alternative estimates of the physical volume indices of GDP and GVA showed lower growth rates compared to official indicators. This is due to the faster growth of alternative estimates of intermediate consumption compared to official ones. In the structure of intermediate consumption, domestic intermediate products were replacing imported analogues. The current dynamics of indicators, to a first approximation, shows signs of localization of production, which may be associated with the transition of enterprises to domestic outsourcing and the implementation of an import substitution policy.At the same time, the presence of measurement problems in the use of double deflation is obvious, most clearly manifested when moving to the analysis of indicators of lower levels of aggregation. The analysis shows in favor of conducting additional research related to the introduction of the double deflation technique in the official methodology.

Identifying the Probability Distribution of Exchange Rates in Sri Lanka

The exchange rate is one of the main components that represents the status of a country’s economic condition. This study mainly focuses on identifying an appropriate distribution that can capture the asymmetric behaviour of important currency exchange rates related to Sri Lanka. The true behaviour of the exchange rates of USD, EURO, JPY, AUD, GBP, CHF, SGD and CAD in terms of LKR was determined using flexible distributions of generalised lambda distribution (GLD), Normal Inverse Gaussian and Skew-Normal. The parameter estimation was carried out by maximum likelihood estimation (MLE), while for GLD, few more parameter estimation techniques were applied. To understand how well the fitted distributions identify the real behaviour of data, we conducted the goodness-of-fit (GOF) tests. The results from Cramer–Von Mises (CvM) and Anderson–Darling (AD) GOF tests pointed out that the exchange rates data follow a GLD with the parameter estimation of maximum product of spacings (MPS). Further, plots of histograms with theoretical densities, cumulative distribution functions (CDFs) with empirical CDF and Quantile–Quantile plots illustrated the same idea. This study presented the findings based on different suitable parameter estimation techniques and this study is the first investigation on the distribution identification of exchange rates in Sri Lanka. JEL Codes: C12,C13,G10

METHODS OF FORMING STUDENTS' CRITICAL THINKING SKILLS THROUGH LITERARY EDUCATION

Given article is dedicated to questions of the shaping the critical thinking pupils in process of the study of the literary product. In her are determined pedagogical conditions of the shaping beside pupils independent estimation of the artistic product, in count, calculate, list which is named interaction of the teacher and pupils in the course of analysis of the artistic text, enrichment pupils literary knowledge, development to independent activity pupils and the main -a critical approach to estimation of the product and his (its) heroes.

UNWTO World Tourism Barometer and Statistical Annex, January 2024

International tourism to reach pre-pandemic levels in 2024 An estimated 1286 million international tourists (overnight visitors) were recorded around the world in 2023, an increase of 34% over 2022. International tourism recovered 88% of prepandemic levels, supported by strong pent-up demand. The Middle East led the recovery by regions in relative terms, being the only region to overcome pre-pandemic levels with arrivals 22% above 2019. Europe reached 94% of pre-pandemic levels in 2023, while Africa recovered 96% and the Americas 90%. Asia and the Pacific reached 65% of pre-pandemic levels, with a gradual recovery since the start of 2023. Four subregions: North Africa, Central America (both +5%), Southern Mediterranean Europe and the Caribbean (both +1%) exceeded pre-pandemic levels in 2023. Total export revenues from tourism (including passenger transport) are estimated at USD 1.6 trillion in 2023, almost 95% of the USD 1.7 trillion recorded in 2019. Preliminary estimates of tourism direct gross domestic product (TDGDP) point to USD 3.3 trillion in 2023, or 3% of global GDP, the same level as in 2019, driven by both domestic and international travel. Following a strong rebound in 2023, international tourism is expected to fully recover pre-pandemic levels in 2024, with initial estimates pointing to 2% growth above 2019 levels in international tourist arrivals. The positive outlook for the sector is reflected in the latest UNWTO Tourism Confidence Index survey, with 67% of tourism professionals indicating better or much better prospects for 2024 compared to 2023. The unleashing of remaining pent-up demand, increased air connectivity, and a stronger recovery of Asian markets and destinations are expected to underpin a full recovery by the end of 2024. Economic and geopolitical challenges continue to pose significant risks to the sustained recovery of international tourism and confidence levels.

Barómetro OMT del Turismo Mundial y anexo estadístico, enero 2024

International tourism to reach pre-pandemic levels in 2024 An estimated 1286 million international tourists (overnight visitors) were recorded around the world in 2023, an increase of 34% over 2022. International tourism recovered 88% of prepandemic levels, supported by strong pent-up demand. The Middle East led the recovery by regions in relative terms, being the only region to overcome pre-pandemic levels with arrivals 22% above 2019. Europe reached 94% of pre-pandemic levels in 2023, while Africa recovered 96% and the Americas 90%. Asia and the Pacific reached 65% of pre-pandemic levels, with a gradual recovery since the start of 2023. Four subregions: North Africa, Central America (both +5%), Southern Mediterranean Europe and the Caribbean (both +1%) exceeded pre-pandemic levels in 2023. Total export revenues from tourism (including passenger transport) are estimated at USD 1.6 trillion in 2023, almost 95% of the USD 1.7 trillion recorded in 2019. Preliminary estimates of tourism direct gross domestic product (TDGDP) point to USD 3.3 trillion in 2023, or 3% of global GDP, the same level as in 2019, driven by both domestic and international travel. Following a strong rebound in 2023, international tourism is expected to fully recover pre-pandemic levels in 2024, with initial estimates pointing to 2% growth above 2019 levels in international tourist arrivals. The positive outlook for the sector is reflected in the latest UNWTO Tourism Confidence Index survey, with 67% of tourism professionals indicating better or much better prospects for 2024 compared to 2023. The unleashing of remaining pent-up demand, increased air connectivity, and a stronger recovery of Asian markets and destinations are expected to underpin a full recovery by the end of 2024. Economic and geopolitical challenges continue to pose significant risks to the sustained recovery of international tourism and confidence levels.

Local existence results in Sobolev spaces for generalized magnetohydrodynamics equations

We consider generalized magnetohydrodynamics (MHD) equations in with fractional diffusions and for the velocity and magnetic field , respectively, where are nonnegative constants and is the fractional Laplacian of order . Using the smoothing effect of for any , we establish local existence results for the generalized MHD equations when the initial data belong to with possibly different orders and . Here, denotes the standard ‐based Sobolev space on of order . To prove our existence results, we also derive new product and commutator estimates in fractional Sobolev spaces which are of independent interest in themselves.

Vertical stratification of phytoplankton biomass in a deep estuary site: implications for satellite-based net primary productivity

The accuracy of satellite estimates for water column net primary productivity (NPP) are contingent upon the reliability of surface phytoplankton biomass, specifically chlorophyll a (Chl.a) and carbon (Cphyt), as indicators of euphotic biomass and photosynthetic rate. We assessed patterns in water column biomass at a deep estuary site (~40 m) in the Firth of Thames, Hauraki Gulf, New Zealand, using ten years (2005-2015) of in situ sampling (40 seasonal voyages and moored instrumentation). Seasonal biomass stratification coincided with physical and chemical stratification and exhibited a reasonable predictability based on surface Chl.a measures from mooring timeseries. High Chl.a (but not Cphyt) accumulated from late-spring (Nov.) in the lower portion of the water column, under nutrient deficient, clear surface water with deep euphotic zone conditions, peaking in mid-summer (Jan.) and ending by early autumn (Mar.). Satellite (MODIS-Aqua) NPP (2002-2018), was estimated with and without correction for deep biomass in two vertically generalized production models (Chl.a-VGPM and Cphyt-CbPM). Mean annual NPP (220-161 g C m-2 y-1, VGPM and CbPM respectively) increased 5-18% after accounting for euphotic zone deep biomass with a mid-summer maxim (Jan.: 30-33%). Interannual anomalies in biomass and NPP (about -10% to 10%) were an order of magnitude greater than small decreasing trends (&amp;lt;&amp;lt; 1% y-1). We discuss the impacts of observational factors on biomass and NPP estimation. We offer contextual insights into seasonal patterns by considering previous observations of biomass trends and nutrient enrichment in the Firth of Thames region. We propose future directions in accounting for deep biomass variations from shallow coastal areas to deeper continental shelf waters.