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In this article, we summarize some new results on r -disjunctive languages and its related topics from some papers, these results form a new progress in this research area. In these results, we show the use of syntactic congruences (resp. syntactic monoids) of languages and the infix languages of languages in studying the characteristics, the decompositions and the classifications of the r -disjunctive languages. In addition, we set out some open problems in this area proposed in these papers.

BackgroundThe pelvic INFIX technique has been proposed as a useful alternative to symphyseal plating for management of unstable pelvic ring injuries. The minimally invasive nature of the procedure, shorter operative time and less perioperative blood loss have been purported as potential advantages.Questions/purposesThis systematic review and meta-analysis were conducted to determine the outcomes and complications of the INFIX technique for unstable pelvic ring injuries.MethodsA systematic review of literature was performed on the PubMed, EMBASE and Scopus databases. Prospective and retrospective studies in all languages, whether comparative or non-comparative, pertaining to the use of INFIX in pelvic fractures were included. Studies which did not evaluate INFIX, case reports, conference abstracts and those with less than 10 cases were excluded. Cadaveric studies, technique papers and studies that did not describe the prespecified outcome measures were also excluded. Meta-analysis consisted of two different arms: a comparative arm, to compare INFIX to symphyseal plating, and a non-comparative meta-analysis arm, to determine pooled rates of outcomes and complications. Risk of bias was determined by the Methodological Index for Non-Randomised Studies (MINORS) tool.ResultsA total of 22 studies were included in the systematic review, of which 7 were comparative and 15 were non-comparative. 746 patients were included for qualitative analysis and pooled analysis done for 589 patients. The average follow-up of these studies ranged from a minimum of 5.4 months to a maximum of 54 months. Comparative meta-analysis (n = 3 studies) of plating and INFIX showed significantly lesser blood loss (mean difference = 176.46 mL; 95% CI − 207.54 to − 145.38) and shorter operative time (mean difference = 26.43 min, 95% CI − 31.79 to − 21.07) with INFIX, but no significant difference in the overall complication rates (OR 1.59, 95% CI 0.83–3.05) and functional outcome scores (mean difference = − 2.51, 95% CI − 5.73 to 0.71). Pooled analysis showed overall good radiological (mean percentage of excellent to good reduction = 91.4%, 95% CI 0.860–0.969) and functional outcomes (mean Majeed score = 86.48, 95% CI 83.34–89.61) with INFIX. The most common complications were lateral femoral cutaneous nerve (LFCN) injury (overall rate 28%, 95% CI 15.1–41%) and heterotopic ossification (HO) (overall rate 9.4%, 95% CI 5.5–13.3%); rates of other complications were low. Significant heterogeneity was noted in the pooled analysis of blood loss, operative time, functional outcome, HO and LFCN injury. The overall strength of evidence was found to be weak.ConclusionThe INFIX technique can be considered as a viable alternative to symphyseal plating for unstable pelvic ring injuries. It has the advantages of shorter operative times and less blood loss, along with comparable functional outcomes, when compared to plating. Overall, good functional outcomes can be expected. However, well-designed, multi-center randomized controlled trials are needed to conclusively prove the benefit of this technique.

Objectives This study aimed to evaluate the effectiveness of 3D-printed guide plate-assisted descending INFIX technology in the management of unstable pelvic ring injuries. Methods This retrospective study analyzed the clinical data of 51 patients who underwent INFIX surgery for pelvic ring fractures at the Second Hospital of Shanxi Medical University between January 2023 and December 2024. Based on the use of 3D-printed guide plates, the patients were divided into two groups: conventional group ( n  = 28) and guide plate group ( n  = 23). The surgical parameters, including operative time, number of intraoperative fluoroscopic evaluations, intraoperative blood loss, and incision length, were recorded and compared between the two groups. The postoperative reduction accuracy was evaluated using the Matta imaging scoring system, while the Majeed scoring system was used to obtain functional outcomes in clinical follow-up. All the potential complications were identified and evaluated accordingly. Results Both the patient groups were followed up for a period of 6–11 months, with an average of 8 months. The guide plate group demonstrated shorter surgery duration, fewer fluoroscopic assessments, and fewer guide needle trajectory adjustments compared to the conventional group ( P  < 0.05). The guide plate group exhibited a higher percentage of good Matta scores than the conventional group (17.39% vs. 14.29%). Conclusions The individualized 3D-printed navigation template significantly reduced the complexity of INFIX surgery, minimized intraoperative and postoperative complications, and enhanced clinical outcomes. The procedure can be safely performed in resource-limited medical facilities, making it feasible for junior surgeons with limited pelvic anatomy experience.

We introduce the infix inclusion problem of two languages S and T that decides whether or not S is a subset of the set of all infixes of T. This problem is motivated by the need for identifying malicious computation patterns according to their semantics, which are often disguised with additional sub-patterns surrounding information. In other words, malicious patterns are embedded as an infix of the whole pattern. We examine the infix inclusion problem for the case where a source S and a target T are finite, regular or context-free languages. We prove that the problem is 1) co-NP-complete when one of the languages is finite, 2) PSPACE-complete when both S and T are regular, 3) EXPTIME-complete when S is context-free and T is regular, 4) undecidable when S is either regular or context-free and T is context-free and 5) undecidable when one of S and T is in a language class where the emptiness of its languages is undecidable, even if the other is finite. We, furthermore, explore the infix inclusion problem for visibly pushdown languages, a subclass of context-free languages.

PurposePelvic ring fractures are challenging injuries and require effective treatment due to the frequently compromised patient condition. The aim of this study was to evaluate the outcome of unstable pelvic ring injuries treated with a minimally invasive pedicle screw–rod system.MethodsRetrospective analysis was performed for patients with an unstable pelvic ring injury that were treated with a minimally invasive anterior internal pelvic fixator (INFIX) with or without a posterior pedicle screw–rod fixator (6/2012–4/2015). The quality of reduction was evaluated by the Tornetta and Matta criteria and the clinical outcome was evaluated by the Majeed scores. Further evaluation included the operation time, intraoperative blood loss, and complication rate.ResultsA total of 23 patients (12 males and 11 females) with a mean age of 37.6 years (range 10–65 years) and a follow-up of 13.5 months (6–27 months) were evaluated. The Tile classification showed 13 type B (B1 = 6, B2 = 4, and B3 = 3) and 10 type C (C1 = 7 and C2 = 3) fractures. Mean operation time and intraoperative blood loss were 24.8 min (20–30 min) and 20.4 ml (16–29 ml) for an anterior INFIX (n = 13), and 60 min (45–70 min) and 150 ml (115–168 ml) when combined with a posterior pedicle screw–rod fixator (n = 10). Quality of reduction was excellent in 13, good in 6, and fair in 4 patients, with no signs of heterotopic ossification. Clinical results after 6 months were excellent in 14 patients, good in 6, fair in 2, and poor in 1. Unilateral thigh paresthesia was seen in 2 patients which resolved after implant removal.ConclusionsThe INFIX appears to be a safe and minimally invasive surgical technique which can effectively be combined with posterior pedicle screw–rod fixation. It also can be applied for the definitive treatment of vertically and/or rotationally unstable pelvic ring injuries, especially in severely compromised patients with a high mortality risk.

Background This study investigated the clinical efficacy of Double INFIX for the treatment of unstable pelvic fractures. Methods We performed a retrospective analysis of 23 patients with unstable pelvic fractures treated using the Double INFIX minimally invasive technique. The cohort included five cases of Tile B1 type, eight cases of B2 type, six cases of B3 type, three cases of C1 type and one case of type C2. Pre- and postoperative evaluations included standardised pelvic serial films and three-dimensional CT scans. Key observational indicators were fracture reduction quality (assessed using Matta’s criteria), fracture healing, functional recovery (evaluated with the Majeed function assessment criteria), and incidence of complications. Results The mean follow-up duration was 24.48 ± 1.78 months. The average fracture healing time was 4.00 ± 1.41 months, and the average time for removal of fixation was 7.43 ± 1.75 months. Repeat imaging at 12 months postoperatively using Matta’s criteria showed eight cases with excellent results (52.17%), 13 cases with good results (34.78%), three cases with fair results (13.04%), and no cases with poor results. The combined excellent and good rate was 86.96%, whereas the fair rate was 13.04%. The average Majeed hip joint function score at the final follow-up was 95.04 ± 1.72. Postoperative complications included meralgia paresthetica in two cases (8.7%) and sacrococcygeal discomfort in three patients when lying flat. Conclusion Double INFIX is a minimally invasive treatment technique with adequate clinical efficacy for managing unstable pelvic fractures.

Background The commonly used technique for treating unstable pelvic fractures with sacroiliac screws and anterior internal fixator (INFIX) is prone to complications, such as injury to the pelvic vasculature and nerves, life-threatening bleeding, lateral femoral cutaneous neuritis, and wound infection. This study investigated the clinical effects of using a modified percutaneous iliosacral screw and INFIX technique for treating unstable pelvic fractures. Methods A retrospective analysis of minimally invasive internal fixation using modified incision of an anterior-ring INFIX application combined with modified percutaneous iliosacral screw placement was performed for 22 cases of unstable pelvic fractures from January 2017 to December 2018. Based on the Tile classification, there were 4 type B1, 7 type B2, 5 type B3 and 6 type C1 injuries. Preoperatively, the length and orientation of the internal fixation were computer-simulated and measured. On postoperative day 3, pelvic radiographs and three-dimensional computed tomograms were used to assess fracture reduction and fixation. All patients were regularly followed up at 4 weeks, 12 weeks, 6 months, 12 months, 24 months and annually thereafter. Fracture healing, complications, visual analogue scale (VAS) scores, the quality of fracture repositioning and Majeed score were assessed during follow-up. Results All patients were followed up for a mean of 25.23 ± 1.48 months. All fractures healed without loss of reduction and no patient showed evidence of delayed union or nonunion. Two years postoperatively, the mean VAS score was 0.32 ± 0.09 and the mean Majeed score was 94.32 ± 1.86. Conclusion The modified percutaneous iliosacral screw technique increases the anterior tilt of the sacroiliac screw by shifting the entry point posteriorly to increase the safety of the screw placement. Downward modification of the INFIX incision reduces the risk of lateral femoral cutaneous nerve injury. This technique is safe, effective and well tolerated by patients.

Objectives . The purpose of this study was to compare the reduction effect and clinical outcomes of anterior subcutaneous internal fixation (INFIX) and steel plate-screw internal fixation in the treatment of anterior ring injury in Tile C pelvic fractures. Methods . In this retrospective study, the clinical outcomes of 46 patients treated using INFIX and 44 patients treated with steel plate-screw internal fixation were analyzed and compared. All patients underwent anterior and posterior fixation. The Matta imaging scoring system was used to evaluate the postoperative reduction accuracy; the Majeed scoring system was applied to obtain functional outcomes in clinical follow-up. All potential complications were identified and evaluated accordingly. Results Both groups of patients were followed up for a period of 13–36 months, with an average of 27 months. The procedure time and blood loss in the INFIX group were significantly lower than those in the plate group(t = − 2.327, P  = 0.023;t = − 4.053, P  = 0.000; there was no statistically significant difference in the Majeed score and Matta score between the two groups after surgery ( P  > 0.05). Conclusions . INFIX treatment for anterior ring injury in Tile C pelvic fractures can achieve good therapeutic effects. Compared to internal fixation with plates and screws, it has advantages such as shorter surgical time and less blood loss. INFIX may be more suitable for obese patients, young women of childbearing age, or patients with urinary system injuries.

Background Treating lateral compression type 1 (LC1) pelvic ring injuries in older patients is controversial. This study evaluated surgical treatments combined with ERAS for treating LC1 pelvic fractures in the elderly. Methods In this retrospective study, patients who underwent surgery with INFIX (supra-acetabular spinal pedicle screws, and a subcutaneous connecting rod; the experimental group) or superior pubic ramus cannulated screw (the control group) fixation of LC1 pelvic fracture from January 2019 to January 2022 were reviewed. Injury radiography and computed tomography were performed to determine the Young–Burgess classification. All patients performed standardized early rehabilitation exercises after surgery and were followed up for > 12 months. After surgery, the Matta score and the visual analog scale (VAS) were evaluated, and the postoperative weight-bearing time and the length of stay (LOS) were recorded. The Barthel index and the Majeed score were evaluated at 4 months after surgery and at the last follow-up. Results Fifty-three patients were included. Thirty-two patients included in the experimental group had a mean age of 75.0 ± 6.2 (range, 66–86) years, and the other 21 patients in the control group had a mean age of 74.6 ± 4.6 (range, 68–83) years. The mean follow-up time was 13.1 ± 1.6 (range, 12–18) months in the experimental group and 13.4 ± 1.3 (range, 12–16) months in the control group. There were no significant differences in follow-up time between the groups ( P  > 0.05). The mean VAS score, time to weight-bearing, and LOS were 2.0 ± 0.7 (range, 1–3), 1.1 ± 0.3 (range, 1–2) d, and 5.8 ± 0.9 (range, 4–7) d in the experimental group and 2.3 ± 1.2 (range, 1–5), 2.5 ± 1.6 (range, 1–7) d, and 6.1 ± 1.6 (range, 5–11) d in the control group, respectively. Between the two groups, there was a significant difference in the postoperative time to weight-bearing ( P  < 0.05), while there was no significant difference in the LOS ( P  > 0.05). No bedrest-related complications occurred in either group. The Matta score was 90.6% in the experimental group and 90.4% in the control group ( P  > 0.05). At the 4-months follow-up, the experimental group had a better Barthel index and Majeed score compared with the control group, which were 86.1 ± 6.2 (range, 70–95) vs. 81.2 ± 4.1 (range, 75–90) and 86.3 ± 3.3 (range, 78–91) vs. 80.3 ± 3.9 (range, 76–86), respectively. The experimental group had better early rehabilitation effect than the control group. There was no significant difference in Barthel index and Majeed score between the two groups at the last follow-up ( P  > 0.05). Conclusion Both INFIX and intramedullary superior pubic ramus cannulated screws can successfully treat LC1 pelvic fractures and reduce bed rest complications among older patients.

Background The Internal Fixator (INFIX) is a popular method, known for its minimal invasiveness and short operation time, for treating anterior pelvic ring fractures. Studies have shown that postoperative complications may occur, including anterolateral femoral cutaneous nerve injury, the femoral nerve paralysis, and delayed fracture healing. These complications are believed to be related to surgical stimulation, an excessively long lateral end of the connecting rod, a small distance between the screw and bone surface, insufficient pre-bending of the connecting rod, and difficulties in fracture reduction. Case presentation We report two unique cases of lower abdominal pseudocyst complicated with suspected infection after INFIX treatment of pelvic fractures at our trauma center. Following surgical removal of the internal fixation, resolution of the cysts was observed in both patients, and subsequent postoperative follow-up revealed the absence of any residual sequelae. These cases have not been reported in previous literature reviews. Discussion The lower abdominal cysts, potentially arising from the dead space created during intraoperative placement of the INFIX rod, may increase infection risk. The etiology remains uncertain, despite the presence of abnormal inflammation markers in both cases, and staphylococcus aureus found in one. These cysts were confined to the lower abdomen, not involving the internal fixation, and hence, only the INFIX was removed. Postoperative oral cefazolin treatment was successful, with resolved pseudocysts and no subsequent discomfort. Conclusion We report two unprecedented cases of post-INFIX abdominal cysts, with a suspected link to intraoperative dead space. Despite uncertain etiology, successful management involved INFIX removal and oral cefixime therapy. These findings necessitate further exploration into the causes and management of such complications.