Explicit Mapping Research Articles

Spatial Memory of BIM and Virtual Reality: Mental Mapping Study

Acquiring accurate spatial memory is critical to many architecture, engineering, construction, and facilities maintenance (AECFM) tasks. The literature has recognized that spatial memory (i.e., the memory of locations and spatial relationships) quality can be affected primarily by visualization methods, i.e., the formats in which spatial information is visualized and presented. In addition to traditional two-dimensional (2D) drawings, emerging visualization methods, such as building information modeling (BIM)-based models and virtual reality (VR), provide more options to visualize complex spatial information in an immersive and interactive way. Although it is well recognized that new visualization methods can benefit performance in many spatial tasks (i.e., tasks that rely or partially rely on spatial memory), there is a lack of explicit evidence about how they affect spatial memory development. Many studies used spatial task performance and spatial memory quality interchangeably, which actually are distinct. This paper presents findings of a mental mapping method (i.e., hand sketching the memorized locations and spatial relationships) to directly measure a person’s spatial memory quality of different building components and layouts. First, a human-subject experiment (n=63) was performed in which participants were instructed to review a building model with varying visualization methods [2D, BIM-based three-dimensional (3D), and VR]. Then participants were required to sketch the memorized building landmarks and layouts as an explicit measure of the spatial memory quality, followed by an inspection task in the real building. The result showed a significant impact of visualization methods on the quality of spatial memory, which was not correlated with the inspection performance. The findings suggest that explicit mental mapping measures instead of final task performance are needed for evaluating spatial memory in AECFM tasks.

The Development Teacher Role and Counseling at Madrasah Ibtidaiyyah

The purpose of this study is to investigate a new approach to develop teachers’ soft skills and provide counseling guidance for students at Madrasah Ibtidaiyah Darud Da'wah wal Irsyad (MI DDI). The research employed a qualitative case study using a bibliographic design with systematic and explicit mapping methods. Data was collected through semi-structured interviews to examine the learning method. The findings show that the innovation role of an Islamic religious education teacher includes counseling activities for students. The collaborative implementation in terms of role between the religious teacher and counselor roles is essential for the successful development of this approach. This research contributes to the development of a new learning method for soft skills and counseling guidance for elementary school students. It demonstrates an effective and efficient strategy to teach and improve teachers’ soft skills by integrating soft skill training into courses focused on hard skills.

Fine-scale mapping of Spartina alterniflora-invaded mangrove forests with multi-temporal WorldView-Sentinel-2 data fusion

Mangrove forests, a critical component of blue carbon ecosystems, make a significant contribution to mitigating climate change and maintaining biodiversity. But in China, they have been suffering from severe invasion by Spartina alterniflora (S. alterniflora). Accurate information on spatial distribution of mangroves and S. alterniflora is a prerequisite to protecting indigenous mangrove ecosystems and managing S. alterniflora invasion. However, the classification performance is often constrained by two major issues: (1) A single-date image, regardless of acquisition time, hardly provides optimal spectral separability among evergreen mangroves, deciduous S. alterniflora and mudflats; (2) Due to the gradual invasion process, the mixtures between land cover classes are prevalent in moderate-resolution images. The use of high-resolution (finer than 2 m) image time series could effectively solve these two issues. However, due to frequent cloud cover in coastal areas and long revisit time of high-resolution satellite sensors, the collection of high-resolution image time series is still a great challenge, let alone substantial expenses. In this study, we proposed a new multi-temporal classification approach to fine-scale mapping of exotic S. alterniflora and native mangroves using synthetic high-resolution image time series derived from spatiotemporal fusion of WorldView-2 and Sentinel-2 data. A total of six synthetic WorldView-2-like images in different phenological periods were produced by the Flexible Spatiotemporal DAta Fusion (FSDAF) method. With the combination of the original and synthetic images, both types of image-based multi-temporal features and pixel-based image compositing features were extracted and evaluated in the following Random Forest classifications. Monte Carlo cross-validation was adopted to provide robust accuracy estimates, and a spatially explicit confidence map was generated to show classification uncertainty and potential errors. In order to further demonstrate the necessity of generating synthetic WorldView-2 images, the entire classification process was repeated using Sentinel-2 images at 10-m spatial resolution and the comparison between fine- and moderate-resolution classification results was made in terms of classification accuracies, classification maps and fractional abundances. Our results show that the spectral profiles of S. alterniflora and mangroves generated from the synthetic WorldView-2 images were consistent with the ones from the paired Sentinel-2 images. Meanwhile, the spatial details of high landscape heterogeneity, unrecognizable in the Sentinel-2 images, were revealed by the synthetic WorldView-2 images. Compared to the single-date classification with the original WorldView-2 image, most of multi-temporal classifications using both the original and synthetic images provided more accurate results, with the overall accuracy raised by up to 3.9%. Among various temporal features adopted in this study, the use of the image-based, stacked spectral reflectance and vegetation index features of all original and synthetic images produced the best classification performance, increasing the producer's and user's accuracies of mangroves, S. alterniflora and mudflats by 2.5%–7.1%. Finally, the Sentinel-2 classification accuracies were generally lower than the WorldView-2 counterparts across all temporal features, with a 6% difference in the highest overall accuracy between the two. Prediction errors of the moderate-resolution classification were often found in heterogeneous landscapes, where S. alterniflora was mixed with mangroves or mudflats. Considering the availability of moderate-resolution data with high revisit frequencies, such as Sentinel-2A/B and Landsat 8/9, future fine-scale mapping exercises might benefit from the multi-temporal classification approach with spatiotemporal fusion of moderate- and high-resolution data, alleviating the problem of the scarcity of high-resolution data in cloudy areas.

Large-scale risk assessment on snow avalanche hazard in alpine regions

Abstract. Snow avalanches are recurring natural hazards that affect the population and infrastructure in mountainous regions, such as in the recent avalanche winters of 2018 and 2019, when considerable damage was caused by avalanches throughout the Alps. Hazard decision makers need detailed information on the spatial distribution of avalanche hazards and risks to prioritize and apply appropriate adaptation strategies and mitigation measures and thus minimize impacts. Here, we present a novel risk assessment approach for assessing the spatial distribution of avalanche risk by combining large-scale hazard mapping with a state-of-the-art risk assessment tool, where risk is understood as the product of hazard, exposure and vulnerability. Hazard disposition is modeled using the large-scale hazard indication mapping method RAMMS::LSHIM (Rapid Mass Movement Simulation::Large-Scale Hazard Indication Mapping), and risks are assessed using the probabilistic Python-based risk assessment platform CLIMADA, developed at ETH Zürich. Avalanche hazard mapping for scenarios with a 30-, 100- and 300-year return period is based on a high-resolution terrain model, 3 d snow depth increase, automatically determined potential release areas and protection forest data. Avalanche hazard for 40 000 individual snow avalanches is expressed as avalanche intensity, measured as pressure. Exposure is represented by a detailed building layer indicating the spatial distribution of monetary assets. The vulnerability of buildings is defined by damage functions based on the software EconoMe, which is in operational use in Switzerland. The outputs of the hazard, exposure and vulnerability analyses are combined to quantify the risk in spatially explicit risk maps. The risk considers the probability and intensity of snow avalanche occurrence, as well as the concentration of vulnerable, exposed buildings. Uncertainty and sensitivity analyses were performed to capture inherent variability in the input parameters. This new risk assessment approach allows us to quantify avalanche risk over large areas and results in maps displaying the spatial distribution of risk at specific locations. Large-scale risk maps can assist decision makers in identifying areas where avalanche hazard mitigation and/or adaption is needed.

Optimal Robust Policy for Feature-Based Newsvendor

We study policy optimization for the feature-based newsvendor, which seeks an end-to-end policy that renders an explicit mapping from features to ordering decisions. Most existing works restrict the policies to some parametric class that may suffer from suboptimality (such as affine class) or lack of interpretability (such as neural networks). Differently, we aim to optimize over all functions of features. In this case, the classic empirical risk minimization yields a policy that is not well-defined on unseen feature values. To avoid such degeneracy, we consider a Wasserstein distributionally robust framework. This leads to an adjustable robust optimization, whose optimal solutions are notoriously difficult to obtain except for a few notable cases. Perhaps surprisingly, we identify a new class of policies that are proven to be exactly optimal and can be computed efficiently. The optimal robust policy is obtained by extending an optimal robust in-sample policy to unobserved feature values in a particular way and can be interpreted as a Lipschitz regularized critical fractile of the empirical conditional demand distribution. We compare our method with several benchmarks using synthetic and real data and demonstrate its superior empirical performance. This paper was accepted by J. George Shanthikumar, data science. Supplemental Material: The online appendix and data are available at https://doi.org/10.1287/mnsc.2023.4810 .

The distribution pattern of pelvic lymph nodal metastases in cervical cancer

PurposeDepiction of pelvic lymph node metastasis (LNM) sites among patients with cervical cancer facilitates accurate determination of the extent of dissection and radiotherapy regimens.MethodsA retrospective study of 1182 cervical cancer patients who underwent radical hysterectomy and pelvic lymph node dissection between 2008 and 2018 was performed. The number of removed pelvic lymph nodes and metastasis status in different anatomical regions was analyzed. The prognostic difference of patients with lymph node involvement stratified by various factors was analyzed by Kaplan–Meier method.Results The median number of pelvic lymph nodes detected was 22, mainly from obturator (29.54%) and inguinal (21.14%) sites. Metastatic pelvic lymph nodes were found in 192 patients, with obturator accounting for the highest percentage (42.86%). The patients with lymph node involvement in single site had better prognosis that those in multiple sites. The overall- (P = 0.021) (OS) and progression-free (P < 0.001) survival (PFS) curves of patients with inguinal lymph node metastases were worse compared to those with obturator site. There was no difference in the OS and PFS among patients with 2 and more than 2 lymph nodes involvement.ConclusionAn explicit map of LNM in patients with cervical cancer was presented in this study. Obturator lymph nodes tended to be involved. The prognosis of patients with inguinal lymph node involvement was poor in contrast to that with obturator LNM. In patients with inguinal lymph node metastases, clinical staging needs to be reconsidered and extended radiotherapy to the inguinal region needs to be strengthened.

Mapping soil organic carbon stocks in Nepal’s forests

Comprehensive forest carbon accounting requires reliable estimation of soil organic carbon (SOC) stocks. Despite being an important carbon pool, limited information is available on SOC stocks in global forests, particularly for forests in mountainous regions, such as the Central Himalayas. The availability of consistently measured new field data enabled us to accurately estimate forest soil organic carbon (SOC) stocks in Nepal, addressing a previously existing knowledge gap. Our method involved modelling plot-based estimates of forest SOC using covariates related to climate, soil, and topographic position. Our quantile random forest model resulted in the high spatial resolution prediction of Nepal’s national forest SOC stock together with prediction uncertainties. Our spatially explicit forest SOC map showed the high SOC levels in high-elevation forests and a significant underrepresentation of these stocks in global-scale assessments. Our results offer an improved baseline on the distribution of total carbon in the forests of the Central Himalayas. The benchmark maps of predicted forest SOC and associated errors, along with our estimate of 494 million tonnes (SE = 16) of total SOC in the topsoil (0–30 cm) of forested areas in Nepal, carry important implications for understanding the spatial variability of forest SOC in mountainous regions with complex terrains.

Dimensionality reduction of large datasets with explicit feature maps

Learning algorithms are often equipped with kernels that enable them to deal with non-linearities in the data, which ensures increased performance in practice. However, traditional kernel based methods suffer from the problem of scalability. As a workaround, explicit kernel maps have been proposed in the past. Previously for the task of streaming Kernel Principal Component Analysis (KPCA), an explicit kernel map has been combined with a matrix sketching technique to obtain scalable dimensionality reduction (DR) algorithm. This algorithm is limited by two issues, both pertaining to the explicit kernel map and the matrix sketching algorithms respectively. As a solution, two new scalable DR algorithms called ECM-SKPCA and Euler-SKPCA are proposed. The efficacy of the proposed algorithms as scalable DR algorithms is demonstrated via the task of classification with many publicly available datasets. The results indicate that the proposed algorithms produce more effective features than the previous algorithm for the classification task. Furthermore, ECM-SKPCA is also demonstrated to be much faster than all other algorithms.

Minimal δ(2)-ideal Lagrangian submanifolds and the quaternionic projective space

We construct an explicit map from a generic minimal δ(2)-ideal Lagrangian submanifold of Cn to the quaternionic projective space HPn−1, whose image is either a point or a minimal totally complex surface. A stronger result is obtained for n=3, since the above mentioned map then provides a one-to-one correspondence between minimal δ(2)-ideal Lagrangian submanifolds of C3 and minimal totally complex surfaces in HP2 which are moreover anti-symmetric. Finally, we also show that there is a one-to-one correspondence between such surfaces in HP2 and minimal Lagrangian surfaces in CP2.

Explicit Relational Reasoning Skills: An Index for Fostering Thinking in Biology Textbooks

Even in the 21st century, textbooks can play a significant role in fostering higher-order thinking skills (HOTs) for effective learning and understanding. Still, HOTs like analogies used in biology textbooks may miss their purpose in promoting in-depth understanding. Since most analogies are presented implicitly or partially explicitly, they lack an explicit mapping to explain the analogical pattern between the source and the target. This study examines the degree to which implicit and explicit expressions of four Relational Reasoning skills (RRs): Analogy, Antinomy, Anomaly, and Antithesis, appear in three biology textbooks taught in Israel's junior high school. Qualitative content analysis crosses four predetermined criteria (C1-C4): RRs' type, texts' type (T1, T2, T3), 'mapping process', and 'use-skill indication'. The quantification of the findings provided information on the RRs' distribution and prevalence. The study's findings indicate that only 14% of texts appear with explicit expressions for RRs, mainly in antinomies questions (T2). Although about 32% of the various texts in biology include instructions for learners to activate HOT by using RRs, they are presented at a partially explicit level. Moreover, less than 2% of activities (T3) explicitly enable HOT by using RRs to solve problems. This study expands the theoretical knowledge of analogies to all four RRs. Methodologically, the study presents explicit mapping processes developed for antinomies, anomalies, and antitheses. The implications of the RRs' degree of explicitness are discussed as an effective index of learners' scientific understanding

Adaptive Identification of Nonlinear Friction and Load Torque for PMSM Drives via a Parallel-Observer-Based Network With Model Compensation

Acquiring accurate knowledge of nonlinear friction and load torque is of great interest for optimizing the control behavior of permanent-magnet synchronous motor (PMSM) drives. In this work, a friction-and-load adaptive identification scheme based on a parallel-observer-based network with model compensation (POBN-MC) is presented. The developed network possesses a parallel structure consisting of the designed two novel observers, which involve a gain-adaptation super-twisting load torque observer and a variable-learning-rate Adaline inertia observer. A non-empirical friction model is proposed to capture friction, forming the model compensation part that is exploited for correcting the torque input of the network. With a two-step mechanism derived from the POBN-MC, the proposed scheme attains the online adaptive identification of the friction and load torque in a manner that integrates both accuracy and simplicity. In the first step, an explicit mapping relationship between the nonlinear friction torque and the rotor speed is determined with the speed response triggered by the natural deceleration. The second step accomplishes the online observation with regard to friction-and-load information matching the real-time operating conditions. Sufficient theoretical analyses, as well as the validations of numerous simulations and experiments, are presented to support the suggested scheme.

Cyclic descents for Motzkin paths

A notion of cyclic descents on standard Young tableaux (SYT) of rectangular shape was introduced by Rhoades, and extended to certain skew shapes by Adin, Elizalde and Roichman. The cyclic descent set restricts to the usual descent set when the largest value is ignored, and has the property that the number of SYT of a given shape with a given cyclic descent set D is invariant under cyclic shifts of the entries of D. Adin, Reiner and Roichman proved that a skew shape has a cyclic descent map if and only if it is not a connected ribbon. Unfortunately, their proof is nonconstructive. Recently Huang constructed an explicit cyclic descent map for all shapes where this is possible.In the earlier version of Adin, Elizalde and Roichman's paper, they asked to find statistics on combinatorial objects which are equidistributed with cyclic descents on SYT of given shapes. In this paper, we explicitly describe cyclic descent sets for Motzkin paths, which are equidistributed with cyclic descent sets of SYT for three-row shapes. Moreover, in light of Stanley's shuffling theorem, we give a bijective proof of the shuffling property of descent statistics for Motzkin paths.

Topological K-theory for discrete groups and index theory

For any countable discrete group Γ (without any further assumptions on it) we first construct an explicit morphism from the Left-Hand side of the Baum-Connes assembly map, Ktop⁎(Γ), to the periodic cyclic homology of the group algebra, HP⁎(CΓ). This morphism, called the Chern-Baum-Connes assembly map, allows in particular to give a proper and explicit formulation for a Chern-Connes pairingKtop⁎(Γ)×HP⁎(CΓ)⟶C.Several theorems are needed to formulate the Chern-Baum-Connes assembly map. In particular we establish a delocalised Riemann-Roch theorem, the wrong way functoriality for periodic delocalised cohomology for Γ-proper actions, the construction of a Chern morphism between the Left-Hand side of Baum-Connes and a delocalised cohomology group associated to Γ which is an isomorphism once tensoring with C, and the construction of an explicit cohomological assembly map between the delocalised cohomology group associated to Γ and the homology group H⁎(Γ,FΓ) (where FΓ is the complex vector space freely generated by the set of elliptic elements in Γ). This last group H⁎(Γ,FΓ) identifies, by the work of Burghelea, as a direct factor of the cyclic periodic homology of the group algebra.Moreover, in this paper Ktop⁎(Γ) stands for the topological K-theory for discrete groups as originally proposed by Baum and Connes in their first paper, where wrong way functoriality in equivariant K-theory was used for its construction. As part of our results we prove that this model is indeed isomorphic to the analytic model for the left-hand side of the assembly map.Our main final theorem gives an explicit geometric index theoretical formula for the above mentioned pairing (without any further assumptions on Γ) in terms of pairings of invariant forms, associated to geometric cycles and given in terms of delocalized Chern and Todd classes, and currents naturally associated to group cocycles using Burghelea's computation. This gives a complete solution, for discrete countable groups, to the problem of defining and computing a geometric pairing between the left hand side of the Baum-Connes assembly map, given in terms of geometric cycles associated to proper actions of the discrete group on manifolds, and cyclic periodic cohomology of the group algebra.

A K3 surface related to Leonardo Pisano’s work on congruent numbers

This note recalls an early 13th century result on congruent numbers by Leonardo Pisano (“Fibonacci”), and shows how it relates to a specific much studied K3 surface and to an elliptic fibration on this surface. As an aside, the discussion reveals how, via explicit maps of degree two, the surface is covered by the Fermat quartic surface and also covers one of the two famous ‘most algebraic K3 surfaces’.

Constructing Faithful Homomorphisms over Fields of Finite Characteristic

We study the question of algebraic rank or transcendence degree preserving homomorphisms over finite fields. This concept was first introduced by Beecken et al. [ 3 ] and exploited by them, and Agrawal et al. [ 2 ] to design algebraic independence–based identity tests using the Jacobian criterion over characteristic zero fields. An analogue of such constructions over finite characteristic fields was unknown due to the failure of the Jacobian criterion over finite characteristic fields. Building on a recent criterion of Pandey et al. [ 15 ], we construct explicit faithful maps for some natural classes of polynomials in the positive characteristic field setting, when a certain parameter called the inseparable degree of the underlying polynomials is bounded (this parameter is always 1 in fields of characteristic zero). This presents the first generalisation of some of the results of Beecken et al. [ 3 ] and Agrawal et al. [ 2 ] in the positive characteristic setting.

A 29-year time series of annual 300 m resolution plant-functional-type maps for climate models

Abstract. The existing medium-resolution land cover time series produced under the European Space Agency's Climate Change Initiative provides 29 years (1992–2020) of annual land cover maps at 300 m resolution, allowing for a detailed study of land change dynamics over the contemporary era. Because models need two-dimensional parameters rather than two-dimensional land cover information, the land cover classes must be converted into model-appropriate plant functional types (PFTs) to apply this time series to Earth system and land surface models. The first-generation cross-walking table that was presented with the land cover product prescribed pixel-level PFT fractional compositions that varied by land cover class but that lacked spatial variability. Here we describe a new ready-to-use data product for climate modelling: spatially explicit annual maps of PFT fractional composition at 300 m resolution for 1992–2020, created by fusing the 300 m medium-resolution land cover product with several existing high-resolution datasets using a globally consistent method. In the resulting data product, which has 14 layers for each of the 29 years, pixel values at 300 m resolution indicate the percentage cover (0 %–100 %) for each of 14 PFTs, with pixel-level PFT composition exhibiting significant intra-class spatial variability at the global scale. We additionally present an updated version of the user tool that allows users to modify the baseline product (e.g. re-mapping, re-projection, PFT conversion, and spatial sub-setting) to meet individual needs. Finally, these new PFT maps have been used in two land surface models – Organising Carbon and Hydrology in Dynamic Ecosystems (ORCHIDEE) and the Joint UK Land Environment Simulator (JULES) – to demonstrate their benefit over the conventional maps based on a generic cross-walking table. Regional changes in the fractions of trees, short vegetation, and bare-soil cover induce changes in surface properties, such as the albedo, leading to significant changes in surface turbulent fluxes, temperature, and vegetation carbon stocks. The dataset is accessible at https://doi.org/10.5285/26a0f46c95ee4c29b5c650b129aab788 (Harper et al., 2023).

Climate vs. nutrient control: A global analysis of driving environmental factors of wetland plant biomass allocation strategy

Wetland plant biomass and its allocation are sensitive to environmental changes, and they make up a significant part of the carbon pool in wetlands. Here, we collected global data on wetland plant biomass from 1980 to 2021. Based on an analysis of 1134 observations from 182 published papers on wetland ecosystems, we generated spatially explicit global maps of belowground biomass (BGB) to aboveground biomass (AGB) ratio of wetland plants. Our study found that AGB is higher in tropical mangrove regions while BGB is higher in cold regions at high latitudes. AGB did not show a significant response to any individual environmental factors (p > 0.05). In the contrast, plant BGB is influenced by total phosphorus (p < 0.05) but not total nitrogen, and extreme temperatures are the main driver of plant BGB (p < 0.05). Compared to climate factors, soil nutrients were the main factor affecting plant biomass allocation in different wetland types. The relationships between the wetland plant biomass and their environmental conditions are discussed, which provided a basis for further understanding the conservation of wetland plants under environmental change.

Satellite solar-induced chlorophyll fluorescence tracks physiological drought stress development during 2020 southwest US drought.

Monitoring and estimating drought impact on plant physiological processes over large regions remains a major challenge for remote sensing and land surface modeling, with important implications for understanding plant mortality mechanisms and predicting the climate change impact on terrestrial carbon and water cycles. The Orbiting Carbon Observatory 3 (OCO-3), with its unique diurnal observing capability, offers a new opportunity to track drought stress on plant physiology. Using radiative transfer and machine learning modeling, we derive a metric of afternoon photosynthetic depression from OCO-3 solar-induced chlorophyll fluorescence (SIF) as an indicator of plant physiological drought stress. This unique diurnal signal enables a spatially explicit mapping of plants' physiological response to drought. Using OCO-3 observations, we detect a widespread increasing drought stress during the 2020 southwest US drought. Although the physiological drought stress is largely related to the vapor pressure deficit (VPD), our results suggest that plants' sensitivity to VPD increases as the drought intensifies and VPD sensitivity develops differently for shrublands and grasslands. Our findings highlight the potential of using diurnal satellite SIF observations to advance the mechanistic understanding of drought impact on terrestrial ecosystems and to improve land surface modeling.

Novel aeroengine fault diagnosis method based on feature amplification

Data-driven fault diagnosis methods have high requirements for data samples. The ideal state is that the input samples have good separability. However, because of the harsh working environment and complex operating conditions, the collected data are highly nonlinear inseparability. The existing methods often cannot achieve a good classification effect. To solve this problem, two feature amplification methods that make full use of the useful information from the aeroengine service data are proposed. One is a high-dimensional mapping method based on explicit mapping of kernel function to amplify features. The other is an experiential method to amplify features. Both methods map the input samples to high-dimensional space to make them more separable in high-dimensional space and retain the useful information of raw data. Each feature after feature amplification still covers strong independent information that can describe fault feature information from different dimensions. Then, four deep learning algorithms that have a good effect on processing time-series data are selected as the classifier. The aeroengine service dataset and the bearing vibration dataset from Case Western University are used to verify the effectiveness of the two feature amplification methods. The experimental results show that the fault diagnosis accuracy can be improved if sample features after high-dimensional mapping possess good orthogonality, otherwise, the accuracy will be reduced.

Berkovich–Uncu Type Partition Inequalities Concerning Impermissible Sets and Perfect Power Frequencies

Recently, Rattan and the first author (Ann. Comb. 25 (2021) 697–728) proved a conjectured inequality of Berkovich and Uncu (Ann. Comb. 23 (2019) 263–284) concerning partitions with an impermissible part. In this article, we generalize this inequality upon considering t impermissible parts. We compare these with partitions whose certain parts appear with a frequency which is a perfect $$t^{th}$$ power. In addition, the partitions that we study here have smallest part greater than or equal to s for some given natural number s. Our inequalities hold after a certain bound, which for given t is a polynomial in s, a major improvement over the previously known bound in the case $$t=1$$ . To prove these inequalities, our methods involve constructing injective maps between the relevant sets of partitions. The construction of these maps crucially involves concepts from analysis and calculus, such as explicit maps used to prove countability of $$\mathbb {N}^t$$ , and Jensen’s inequality for convex functions, and then merge them with techniques from number theory such as Frobenius numbers, congruence classes, binary numbers and quadratic residues. We also show a connection of our results to colored partitions. Finally, we pose an open problem which seems to be related to power residues and the almost universality of diagonal ternary quadratic forms.